Problem 1E: Evaluating the Derivative of an Inverse Function Given the point (x1,y1) on the graph of y=f(x),... Problem 2E: Inverse Trigonometric Functions Are the Derivatives of the inverse transcendental functions... Problem 3E: Evaluating the Derivative of an Inverse Function In Exercises 3-12, verify that / has an inverse... Problem 4E: Evaluating the Derivative of an Inverse Function In Exercises 3-12, verify that f has an Inverse... Problem 5E: Evaluating the Derivative of an Inverse Function In Exercises 3-12, verify that f has an Inverse... Problem 6E: Evaluating the Derivative of an Inverse Function In Exercises 3-12, verify that f has an Inverse... Problem 7E: Evaluating the Derivative of an Inverse Function In Exercises 3-12, verify that f has an Inverse... Problem 8E: Evaluating the Derivative of an Inverse Function In Exercises 3-12, verify that f has an Inverse... Problem 9E: Evaluating the Derivative of an Inverse Function In Exercises 3-12, verify that f has an Inverse... Problem 10E: Evaluating the Derivative of an Inverse Function In Exercises 3-12, verify that f has an inverse... Problem 11E: Evaluating the Derivative of an Inverse Function In Exercises 3-12, verify that f has an inverse... Problem 12E: Evaluating the Derivative of an Inverse Function In Exercises 3-12, verify that f has an inverse... Problem 13E: Graphs of Inverse Functions Have Reciprocal Slopes In Exercises 13-16, show that the slopes or the... Problem 14E: Graphs of Inverse Functions Have Reciprocal Slopes In Exercises 13-16, show that the slopes or the... Problem 15E: Graphs of Inverse Functions Have Reciprocal Slopes In Exercises 13-16, show that the slopes or the... Problem 16E: Graphs of Inverse Functions Have Reciprocal Slopes In Exercises 13-16, show that the slopes or the... Problem 17E: Finding a Derivative In Exercises 17-42, find the derivative of the function. f(x)=arcsin(x1) Problem 18E Problem 19E: Finding a Derivative In Exercises 17-42, find the derivative of the function. g(x)=3arccosx2 Problem 20E: Finding a Derivative In Exercises 17-42, find the derivative of the function. f(x)=arcsec2x Problem 21E: Finding a Derivative In Exercises 17-42, find the derivative of the function. f(x)=arctanex Problem 22E: Finding a Derivative In Exercises 17-42, find the derivative of the function. f(x)=arccotx Problem 23E: Finding a Derivative In Exercises 17-42, find the derivative of the function. g(x)=arcsin3xx Problem 24E: Finding a Derivative In Exercises 17-42, find the derivative of the function. g(x)=arccosxx+1 Problem 25E: Finding a Derivative In Exercises 17-42, find the derivative of the function. g(x)=e2xarcsinx Problem 26E: Finding a Derivative In Exercises 17-42, find the derivative of the function. h(x)=x2arctan5x Problem 27E: Finding a Derivative In Exercises 17-42, find the derivative of the function. h(x)=arccot6x Problem 28E: Finding a Derivative In Exercises 17-42, find the derivative of the function. f(x)=arccsc3x Problem 29E: Finding a Derivative In Exercises 17-42, find the derivative of the function. h(t)=sin(arccost) Problem 30E: Finding a Derivative In Exercises 17-42, find the derivative of the function. f(x)=arcsinx+arccosx Problem 31E: Finding a Derivative In Exercises 17-42, find the derivative of the function. y=xarccosx2x Problem 32E: Finding a Derivative In Exercises 17-42, find the derivative of the function. y=lnt2arctant2 Problem 33E: Finding a Derivative In Exercises 17-42, find the derivative of the function. y=lnx+1x1+arctanx Problem 34E Problem 35E: Finding a Derivative In Exercises 17-42, find the derivative of the function. g(t)=tan(arcsint) Problem 36E: Finding a Derivative In Exercises 17-42, find the derivative of the function. f(x)=arccscx+arccscx Problem 37E: Finding a Derivative In Exercises 17-42, find the derivative of the function. y=xarcsinx+1x2 Problem 38E: Finding a Derivative In Exercises 17-42, find the derivative of the function. y=xarctan2x14ln(1+4x2) Problem 39E: Finding a Derivative In Exercises 17-42, find the derivative of the function. y=8arcsinx4x16x22 Problem 40E: Finding a Derivative In Exercises 17-42, find the derivative of the function. y=25arcsinx5x25x2 Problem 41E: Finding a Derivative In Exercises 17-42, find the derivative of the function. y=arctanx+x1+x2 Problem 42E: Finding a Derivative In Exercises 17-42, find the derivative of the function. y=arctanx212(x2+4) Problem 43E: Finding an Equation of a Tangent Line In Exercises 43-48, find an equation of the tangent line to... Problem 44E: Finding an Equation of a Tangent Line In Exercises 43-48, find an equation of the tangent line to... Problem 45E: Finding an Equation of a Tangent Line In Exercises 43-48, find an equation of the tangent line to... Problem 46E: Finding an Equation of a Tangent Line In Exercises 43-48, find an equation of the tangent line to... Problem 47E: Finding an Equation of a Tangent Line In Exercises 43-48, find an equation of the tangent line to... Problem 48E: Finding an Equation of a Tangent Line In Exercises 43-48, find an equation of the tangent line to... Problem 49E: Finding an Equation of a Tangent Line In Exercises 49-52, (a) find an equation of the tangent line... Problem 50E: Finding an Equation of a Tangent Line In Exercises 49-52, (a) find an equation of the tangent line... Problem 51E: Finding an Equation of a Tangent Line In Exercises 49-52, (a) find an equation of the tangent line... Problem 52E: Finding an Equation of a Tangent Line In Exercises 49-52, (a) find an equation of the tangent line... Problem 53E: Tangent Lines Find equations of all tangent lines to the graph of f(x)=arccosx that have slope 2. Problem 54E: Tangent Lines Find equations of all tangent lines to the graph of f(x)=arctanx that have slope 1/4. Problem 55E: Linear and Quadratic Approximations The linear and quadratic approximations of a function f at x=a... Problem 56E Problem 57E Problem 58E Problem 59E Problem 60E Problem 61E Problem 62E Problem 63E Problem 64E: Finding the Equation of a Tangent Line In Exercises 63-66, use implicit differentiation to find an... Problem 65E Problem 66E Problem 67E: Exploring concepts Inverse Secant-Function Some-calculus-textbooksdefine the-inverse-secant using to... Problem 68E: Derivatives of Inverse Trigonometric Functions Determine whether the derivative of each inverse... Problem 69E: Tangent Lines Consider the tangent line j to the graph of f at any point (a. b) and the tangent line... Problem 70E: HOW DO YOU SEE IT? Use the information in the graph of f below. (a) What is the slope of the tangent... Problem 71E: Think About It The point (1, 3) lies on the graph of f, and the slope of the tangent line through... Problem 73E: Angular Rate of change An airplane-flies-at'an-altitudeof-5 -miles toward a point directly f over... Problem 74E: Angular Rate of Change Repeat Exercise 73 for an altitude of 3 miles and describe how the altitude... Problem 75E: Angular Rate of Change In a free-fall- experiment, an object is dropped from a height of 256 feet, A... Problem 76E: Angular Rate of Change A television camera at ground level is filming the lift-off of a rocket at a... Problem 77E: Angular Rate of Change An observer is standing 300 feet from the point at which a balloon is... Problem 78E: Angular Speed A patrol car is parked 50 feet from a long warehouse (see figure). The revolving light... Problem 79E Problem 80E Problem 81E Problem 82E Problem 83E Problem 84E Problem 85E Problem 86E format_list_bulleted