Suppose h(x) =log,(3x+1). What is the correct result Зх + %3D of the derivative of h with respect to x? 3ln (2) Ah'(x) %3D Зх + 1 1 h'(x) = 3(3к + 1) In (2) In (2) © h'(x)=- 3(3x+1) C h'(x) = - (3x+1) In (2)

Q: Find the derivative of f(x) = COS 4 log3 (x²) os(5x)

A: Explanation of the answer is as follows

Q: Solve for the derivative of x² – y² = 9 using implicit differentiation %3D

A: Given :                x2 - y2 = 9To find :                 y'

Q: FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORM 2. y = 2 Arccos (1-x/2)+ Square root of…

A: Second order derivative.

Q: Shows the derivative function of: 2x² + ln x²(2x² + 5x − 1)

A:

Q: Suppose we want to use logarithmic differentiation to calculate the derivative of y=x²x . As a first…

A:

Q: Find the derivative of Log(2z³). 2/z 2/2? 1/2? 3/z

A: Answer

Q: what would be the output if the 2nd derivative is negative

A: We know that for a function y = f(x), the points of extremum are obtained if the first derivative of…

Q: Find the derivative of k(x) = log3(x) cos

A:

Q: In(x²) What is the derivative of

A:

Q: Compute the derivative in terms of log for y=log(xe^(-3x))

A:

Q: What is the first derivative of s(x)=(6x)^3x at x=3? Enter an exact answer in terms of a natural…

A: We will take the logarithm with base e and then find the derivative with respect to x and then…

Q: 4. Find the 2nd derivative of f(x)=14-x (x)%3D

A: The give function is fx=4-x

Q: 2.) Find 1st derivative of y = e-'In (x-1)

A:

Q: Obtain the second derivative of the function f(x) = 6 In(8x) – 3z4 and state the value of this…

A:

Q: Determine the first derivative of the ff. function 1 + In(3x?) y : 1+ In(4x)

A: the given function is: y=1+ln3x21+ln4x we have to determine the first derivative of the given…

Q: Determine the first derivative of the ff. function y = 2 + arctan(3 sec 2x)

A: We have to find the first derivative of the function: y=2+tan-13 sec 2x We know the formula of…

Q: S(x)= Jx-5

A: given that f(x)=1x-5 find the derivative from first principle f'x=limh→0 fx+h-fxh

Q: Find the derivative: y = 6 In x 6 ln x-1 x7 1-6 ln x 12 1+6 ln x x12 4 O 1-6 ln x x7 O

A:

Q: Determine the derivative of y = ln(4x² - 2x). O 8x-2 4x-1 8x-2 4x²-x 4x-1 4x²-x 4x-1 2x2- -x O O

A:

Q: Log Activity CALL l.y=log4 (3x2 -5x) In 9x4 2.y= 3.y= Inx3 X-5

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: y = ln(24) 2x-4 O 4x-x² 2x-4 x²-4x 4 4x-x² 4 x²-4x O о O 8

A:

Q: 11) Find the first derivative of y = (lnx) 4

A:

Q: Find the first derivative of y = 1 using the Chain Rule. (1– x4)6

A: These questions are related to differentiation, We will solve them using given information.

Q: 2. Determine the second derivative of f(x) = x²e²* at x = -2 with a step-size of h=0.50 using…

A: Given function f(x)=x2e2x. The objective is to determine the second derivative of fx at x=-2 with a…

Q: Suppose that the first derivative of y = ƒ(x) is y'= 6x(x + 1)(x - 2). At what points, if any, does…

A: The derivative of the function y=f(x) is y'=6xx+1x-2. We have to find at what points, if any, does…

Q: Find the derivative OF the exponential funchion y = In ( 5- e **) Please simplify it Further.

A: Consider the provided equation, y=ln5-e4x Find the derivative of the equation. Apply the chain rule…

Q: 1. 8rd Derivative of fC x) = 4 x³ - 8x5 1

A: We will use just the basic knowledge of differential calculus to answer this question step-wise.

Q: Derive a formula that approximates the second derivative of the function sampled at x = 0, 0.01,…

A: Let us assume that second derivative function  f"x0=Afx0+Bfx0-h+Cfx0+2h can be rewritten as…

Q: What is the value of the second derivative y" at the point (4,3)

A:

Q: Find the derivative of y = log2 4x Ox/In4 O 1/xln4 O4/1n4 @ 4/xin4

A: To solve the following problem

Q: solve the first and second derivative of Y= (1+lnx)  /  x

A: If y=f(x), then the independent variable x is called the input of the function, and the dependent…

Q: Compute the derivative of (ln x)^ln x

A: To find the derivative of (ln x)ln x Using the exponent rule ab=eb ln a we get, (ln x)ln x=e(ln x)ln…

Q: Determine the second derivative of f(x) = x²e²x at x = -2 with a step-size of h=0.50 using Central…

A:

Q: Use Delta method to find the derivative of e*

A:

Q: Shows the derivative function of: x³  + ln x(3x² + 5)

A:

Q: what is the second derivative of -y/x

A: Apply the quotient rule, If f=uv,thenddxf=vdudx-udvdxv2 If f=-yx, where y is the dependent variable,…

Q: Find the derivative of f(x) = log(-6x* – 6x + 5) at the point x = 2. Provide your answer below:…

A:

Q: Find the derivative of the function. 8 f(x) =x" log 6x .7 ,7 O A. X +8x log ,x .7 O B. In 6 + 8x log…

A: According to product rule of differentiation ddxuv=vddxu+uddxv and according to power rule of…

Q: Suppose we are asked to compute the 100th derivative of x 3 . How can we obtain the answer in a fast…

A: Solve the following

Q: Find the first derivative of x² + 3xy + y3 = 10 implicitly.

A: The given function x2+3xy+y3=10

Q: Find and sketch an exponential equation of the form y = Cekx that passes through the points (0, 8)…

A: Given an exponential equation of the form y=Cekx that passes through the points (0,8) and (3,4). To…

Q: Find the derivative of f (x) = In(3x² – x)³ in two different ways; (a) with the chain rule %3D | and…

A: Given fx=ln3x2−x3aUsing Chain Rulelnfx'=1fxf'xDifferentiate w.r.t…

Q: Find the second derivative of y=x-1 at x=2

A:

Q: Suppose that the second derivative of the function y = ƒ(x) is y'' = x2(x - 2)3(x + 3). For what…

A: Given that, y=f(x) Second Derivative is y'' = x2(x - 2)3(x + 3). As we know that, Inflection point…

Q: 4. Find the 2nd derivative of f (x) = 4-x x)%3)

A: To determine the second derivative of the function given by; f(x)=4-x Differentiate the function…

Q: 3) Determine the second derivative of y = 5x* + 4x -+÷-3 2x2

A:

Q: What is the derivative of y = log, sec(e²x) Dxy = 2 e² tan (²) Dxy = 2 (log, e) e²x sec(e) tan(e) D,…

A:

Q: Find the equation of the tangent line to the curve y = log(x2-3x+1) at the point (3,0)

A: