Determine h(1) and h'(1). h(x) = [f (x)]2

Q: i. y= ) In (x+3

A:

Q: Find the derivative using the chain rule: x(x^2+1)^(-1/2)

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 second derivative for the functions defined as follows g(x) = 4x(ln x)

A: We have to find second derivative of the function: gx=4x lnx Since two function are in product so we…

Q: 5. Find the derivative of: a. f(x) = cos(e³x-4)

A:

Q: Find y" by implicit differentiation. x² + 4y² = 4

A:

Q: Find the derivative of: 9e 7sin ( 3x*) Use e^x for e". -

A: We use chain rule to find the derivative.

Q: Find the first derivative of g(x) = - 9e* tan(x). : (x),6

A:

Q: Compute the derivative of f(x) = 7 ln (x + 10) + In (x³ ): Answer: f'(x) =

A: Given function is  f(x)= 7ln(x+10) + ln(x3), we have to find the derivative of f(x) with respect to…

Q: 4) Find the derivative of the function: x* cos x h(x) %3D Vx2 + 1

A: Answer

Q: ; Compute the derivative of the function: f (x) = (+ Inx)² а.

A:

Q: y = In- e 2x+1

A:

Q: 2) Find the derivative of the function f(x) = (x³ – tan(4x² – 2)* |

A: Given :            To find the derivative of the given function                f(x) = x3 -…

Q: Find the derivative of the function.

A: Given that, f(x)=ln(x-1)   As we know, ddxln(x)=1x Chain Rule Of derivative, If…

Q: 8. Find the derivative of the function. y= In(1+x)

A:

Q: Find the most general anti-derivative of f(x) = 9Vx +1+ cos x.

A:

Q: Compute the indicated derivative using the chain rule. X = 4 + 3t, y = -7t; Oy

A:

Q: Find the derivative of the function f(x) = 5ª+x² + log3 (In x). %3D

A: To find the derivative of the given function.

Q: Find the derivative of the function.

A: Consider the given function as y=xtan-12x-14ln1+4x2

Q: 1 14) Use the definition of derivative to find dx 3- х.

A:

Q: 6. Find the first order derivative with respect to z of the function u = In/x2 + y2 +z²

A:

Q: 3/x +1 f(x) = X+2 at x = -1

A:

Q: Determine the derivative of g ( x ) = 3 e-4 x*sin(7 x) with respect to x. = (x), 6

A: As per the guidelines, we need to author the 1st question.  We know that product rule is given by…

Q: Use three-point midpoint formula to evaluate the first derivative of y=x2+5x−1y=x2+5x−1 at x=0x=0…

A: Given function is y=x2+5x−1. We have to evaluate the first derivative of y=x2+5x−1 at x=0 using a…

Q: Shows the derivative function of: u³ + 2u, where u = x² + 3

A: Let's find.

Q: Let y = x(ln x)² – 2x In x. Find the value of X for which the second derivative, y" (x), equals…

A: Solve the following

Q: In(3x) Find the derivative with respect to x of y 3x

A: We will use the quotient rule of differentiation to find the derivative of y. Chain rule of…

Q: 5. Find the first order derivative with respect to y of the function U = In/x² + y² + z²

A:

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = x4/4 ln x - x4/16

A:

Q: Find the derivative of f(z) = 3+ 2x² – 2y² + i4xy .

A: We find out the derivative of given function .we differentiate both sides with respect to z and take…

Q: Find the weak derivative of f() = |x² – x + 1/5| on the 1) interval (0,1).

A:

Q: 1- Solve the second derivative forf(x, y,z) = e sinay3) əx2

A:

Q: Find the derivative of the function. f(x) = ln 2x/(x + 3)

A:

Q: 1. Y= 3x -x- 2

A: Find your answer below

Q: 9. Find the derivative of the function using chain rule. f(t) = 3t In t

A: To find the derivative of the function

Q: Find the derivative of the function  f(x)= e^-3x ln x

A: Given function is

Q: Find the derivative of the function. f(x) = ln(x2 + 3)

A:

Q: Find the derivative of the function y, below. 9x(ln x + In 2) – 8x + v2 %3D

A: first, simplify the function  y=9xlnx+ln2-8x+2 y=9xlnx·2-8x+2 y=9xln2x-8x+2

Q: 4. F(x) = (1-t) dt

A: To find the first derivative

Q: Find the derivative of the following using the three-step rule 2. y=Va² +x

A:

Q: Find the derivative of the function.   y = In(x)/x9

A:

Q: 1. Find the first order derivative of u = x*.

A:

Q: Find all possible functions with the given derivative. = రx = 1x 2x

A: The answer is given below

Q: 5. Find derivative of the following composite function using the Chain Rule: f(x) = 3x2 + 8x, x(t) =…

A:

Q: Shows the derivative function of: 2u² + 5u, where u = x² + 3x

A: Given:     To determine: derivative of the given function.

Q: Find the derivative of f(x)= ln x^2/x^2+1

A:

Q: In x g(x) = 2

A: