2. Let f(x) = x² In a + 1. Use the second derivative formula to approximate f"(1) when h = 0.2. %3D %3D

Q: Find the nth derivative of the function y=xex at x=0.

A: To find the nth derivative of function y.

Q: 2. Compute the derivative of the following functions: 1-e-* (a) f(x) = V1 – sin³ x, (b) f(x) =

A:

Q: 1 The derivative of the function y = cos V at z e = is equal to 4.

A:

Q: Solve the first derivative of f(x) = e-2x In x at x 0.5 using forward finite-divided difference and…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the derivative of y with respect to x. y = In (tan 1(5x)) dy dx

A:

Q: Find the derivative of y with respect to the independent variable. COS y = 10 cos ( OA. -10 COS TO…

A:

Q: Show that the function f(t) = sin(e*) is of exponential order as t → +oo but that its derivative is…

A: To show that the given function ft=sinet2 is of exponential order.

Q: Assume mmh (x) = f(g(x)) such that the first an exist g Second derivatives of both of and What is b"…

A: Assume h(x) = f(g(x)) such that the first and second derivatives of both f and g exist  We have to…

Q: 1. Compute forward approximations of O(h) and O(h² for the first derivative of y = e* evaluated at x…

A: 1st we will derive formula for O(h) and O(h2) and then find corresponding values

Q: In (3x) Find the derivative of y with respect to x if y= sin (7 e') dt. dy dx

A: Given : A function is given as: y=∫0ln3xsin7etdt To find : The derivative of the function y.…

Q: Suppose In (x + 2y) = x*. Use implicit differentiation to find the derivative of y with respect to…

A:

Q: Find the derivative of y with respect to 1. y = In V4x2 + 7x %3D 2. y = sec?(e-4*)

A: A detailed solution is given below.

Q: Can you help me with this problem step by step?

A: To determine the derivative of given function.

Q: In (In e*1): What is the derivative of y 3z²+1

A:

Q: Solve for the following implicit derivative: d²y si sen(y) = ycos(2x) dx?

A: We have to find the double derivative of the given function.

Q: Find the derivative of f (x) = Ln e*+1 using the limit process. %3D

A:

Q: 1. f(x) =In (ta n"x)

A: Given query is to find the first derivative of the expression.

Q: Compute forward difference approximations for the first derivative of the function, y =[ eln(x)2, at…

A:

Q: Find the derivative at the given point. f(x)= at x = 0 %3D x+1 O 1/4 O-1

A:

Q: Find the derivative of the function

A: Given function, Fx=∫πlnxcoset dt

Q: Consider the derivative function h (x) = -sec? (x) + 9. What is the general antiderivative of h?

A:

Q: What is the 4th derivative at x = 0 of the function f(z) = (2r + 1)* %3D

A:

Q: Find the derivative of the function. r sin(x) y = Jcos(x) In(4 + 9v) dv y'(x) = %3D

A:

Q: What is the derivative of * In(xy) = e"y – arccos(xy)?

A: We differentiate given equation

Q: Evaluate the derivative of mq4.4.png cosh (bVx3 f(x) = a ln sinh(cx2) if a = 69, b = 0.6, and c = 6…

A: Given function: fx=alncoshbx3sinhcx2 To find: The derivative of the function f'(7) using…

Q: 4 For the function y = 1 e - dy the second order derivative dx? is

A: Given that a function and find second derivative of this function (d2y/dx2). We know that d(xn)/dx =…

Q: Find the second derivative 1. y = In(x^3+1) 2. y = Arctan (e^x)

A: Given: y=lnx3+1, y=tan-1ex

Q: 3. The derivative of f(x) = In x at x = 3 when h = 0.002

A: 3) To find the true error and relative error of the function: f(x)=ln x, x=3 & h=0.002

Q: In (1 + 2), What is the derivative of y .? e2z %3D

A:

Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = 4, 8'(2) = 5, and g"(2) =…

A: Given: The function singx with g2=π4, g'2=5, and g''2=3, To find: The second derivative of given…

Q: 2. Prove from the definition of derivative that for n EZ, d ng"-1 dr

A:

Q: Find the derivative y = e* In x In x ex E + e* In x O None of these

A: Use product rule:-

Q: D-the derivative is y = In In (VW) 1 +

A: The objective of the question is determine the derivative of the given function.

Q: 3. Use the forward-difference formula to approximate the derivative of f (x)=sin(In x) at x, = 2.5…

A: The derivative of the function can be calculated using the difference method. The formula for the…

Q: Compute the high-accuracy central difference approximation for the first derivative of the function…

A:

Q: Use backward, forward, and centered difference approximation to estimate the second derivative of…

A:

Q: In (4x) Find the derivative of y with respect to x if y = sin (8 e') dt.

A:

Q: In x 3. Compute the approximate derivative of f(x) = · at x = 2, using three-midpoint x² + 1 formula…

A: Given is a function and at a point at which the approximate value of first derivative of the…

Q: 4. Show that the derivative of log,(Va +5) is 3(r + 5) In(2)

A:

Q: Calculate the derivative of the following function. 3. 9X y3D 4x+1 dy dx

A:

Q: Find the derivative of the following function. y= In (In (4x)) dy dx

A:

Q: (4)The instantaneous rate of change of f(r) = e- at a = 1 is . .. (5) The derivative of f(x) = sec2…

A: (4) We have So we get the instantaneous rate of change of the function at  as .

Q: Compute the second derivative with respect to r of 3x + 8 y = at x = 1.

A:

Q: 2 e -8; x(0) = 1 dt

A: Solution is given below:

Q: In (3x) Find the derivative of y with respect to x if y = sin (7 e') dt. %3D dy dx

A: Given y=∫0ln3xsin7etdt.We need to find dydx

Q: Use backward, forward , and centered difference approximation to estimate the second derivative of…

A: The formulas for the backward, forward, and central differences to approximate the second derivative…

Q: Suppose x6 e-5y = In (xy). Find Y by implicit differentiation. dx

A:

Q: Compute the derivative of h(sin(x)) at æ = 1/6, assuming h'(0.5) 4: %3D

A: As we know that; The Chain Rule: fgx'=f'gx·g'x Let, hfx=hsinx

Q: The derivative of f(z) = Log(2iz - 4+6i) at z = -3+i is

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: