Problem 1E: Evaluating the Derivative of an Inverse Function In Exercises 110, verify that f has an inverse.... Problem 2E: Evaluating the Derivative of an Inverse Function In Exercises 110, verify that f has an inverse.... Problem 3E: Evaluating the Derivative of an Inverse Function In Exercises 110, verify that f 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: Graphs of Inverse Functions Have Reciprocal Slopes In Exercises 13-16, show that the slopes or the... Problem 12E: Graphs of Inverse Functions Have Reciprocal Slopes In Exercises 13-16, show that the slopes or the... 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 23E: Finding a Derivative In Exercises 2348, find the derivative of the function. f(x)=arcsin(x+1)... Problem 24E: Finding a Derivative In Exercises 2348, find the derivative of the function. f(x)=arcsin(x+1)... Problem 25E: Finding a Derivative In Exercises 17-42, find the derivative of the function. g(x)=3arccosx2 Problem 26E: Finding a Derivative In Exercises 17-42, find the derivative of the function. f(x)=arcsec2x Problem 27E: Finding a Derivative In Exercises 17-42, find the derivative of the function. f(x)=arctanex Problem 28E: Finding a Derivative In Exercises 17-42, find the derivative of the function. f(x)=arccotx Problem 29E: Finding a Derivative In Exercises 17-42, find the derivative of the function. g(x)=arcsin3xx Problem 30E: Finding a Derivative In Exercises 17-42, find the derivative of the function. g(x)=arccosxx+1 Problem 31E: Finding a Derivative In Exercises 17-42, find the derivative of the function. g(x)=e2xarcsinx Problem 32E: Finding a Derivative In Exercises 17-42, find the derivative of the function. h(x)=x2arctan5x Problem 33E: Finding a Derivative In Exercises 17-42, find the derivative of the function. h(x)=arccot6x Problem 34E: Finding a Derivative In Exercises 17-42, find the derivative of the function. f(x)=arccsc3x Problem 35E: Finding a Derivative In Exercises 17-42, find the derivative of the function. h(t)=sin(arccost) Problem 36E: Finding a Derivative In Exercises 17-42, find the derivative of the function. f(x)=arcsinx+arccosx Problem 37E: Finding a Derivative In Exercises 17-42, find the derivative of the function. y=xarccosx2x Problem 38E: Finding a Derivative In Exercises 17-42, find the derivative of the function. y=lnt2arctant2 Problem 39E: y=12(12lnx+1x1+arctanx) Problem 40E: y=12[x4x2+4arcsin(x2)] Problem 41E: Finding a Derivative In Exercises 17-42, find the derivative of the function. g(t)=tan(arcsint) Problem 42E: Finding a Derivative In Exercises 17-42, find the derivative of the function. f(x)=arccscx+arccscx Problem 43E: Finding a Derivative In Exercises 17-42, find the derivative of the function. y=xarcsinx+1x2 Problem 44E: Finding a Derivative In Exercises 17-42, find the derivative of the function. y=xarctan2x14ln(1+4x2) Problem 45E: Finding a Derivative In Exercises 17-42, find the derivative of the function. y=8arcsinx4x16x22 Problem 46E: Finding a Derivative In Exercises 17-42, find the derivative of the function. y=25arcsinx5x25x2 Problem 47E: Finding a Derivative In Exercises 17-42, find the derivative of the function. y=arctanx+x1+x2 Problem 48E: Finding a Derivative In Exercises 17-42, find the derivative of the function. y=arctanx212(x2+4) Problem 49E: Finding an Equation of a Tangent Line In Exercises 43-48, find an equation of the tangent line to... Problem 50E: Finding an Equation of a Tangent Line In Exercises 43-48, find an equation of the tangent line to... Problem 51E: Finding an Equation of a Tangent Line In Exercises 43-48, find an equation of the tangent line to... Problem 52E: Finding an Equation of a Tangent Line In Exercises 43-48, find an equation of the tangent line to... Problem 53E: Finding an Equation of a Tangent Line In Exercises 43-48, find an equation of the tangent line to... Problem 54E: Finding an Equation of a Tangent Line In Exercises 43-48, find an equation of the tangent line to... Problem 15E: Finding an Equation of a Tangent Line In Exercises 49-52, (a) find an equation of the tangent line... Problem 16E: Finding an Equation of a Tangent Line In Exercises 49-52, (a) find an equation of the tangent line... Problem 17E: Finding an Equation of a Tangent Line In Exercises 49-52, (a) find an equation of the tangent line... Problem 18E: Finding an Equation of a Tangent Line In Exercises 49-52, (a) find an equation of the tangent line... Problem 55E: Tangent Lines Find equations of all tangent lines to the graph of f(x)=arccosx that have slope 2. Problem 56E: Tangent Lines Find equations of all tangent lines to the graph of f(x)=arctanx that have slope 1/4. Problem 57E: Linear and Quadratic Approximations The linear and quadratic approximations of a function f at x=a... Problem 58E Problem 59E Problem 60E Problem 19E Problem 20E Problem 21E Problem 22E Problem 61E Problem 62E: Finding the Equation of a Tangent Line In Exercises 63-66, use implicit differentiation to find an... Problem 63E Problem 64E Problem 65E Problem 66E Problem 67E Problem 68E Problem 69E 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 72E Problem 72E 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: Existence of an Inverse Determine the values of k such that the function f(x) = kx + sin x has an... Problem 81E Problem 82E Problem 83E Problem 84E Problem 85E Problem 86E Problem 87E Problem 88E format_list_bulleted