See attached first.  The function h is given by h(x)=cos(kx)f(x) for all real numbers,  where k is a constant.  Find h'(x) and write an equation for the line tangent to the graph of h at x=0.

Q: Which of the following functions is always equal to its (first) derivative? O a) In(x) O b) e5æ O c)…

A:

Q: Find a formula for df 1 dx for the function below using the Derivative Rule for Inverses. f(x) = (5…

A: Given,         fx=5-3x3We know that,           The Derivative Rule for inverses is given by…

Q: Determine the first derivative for each of the following functions. Remember to "Tidy" up your final…

A:

Q: 1) Find the derivatives of the following. Simplify your final answers. d) l(x) = tanh-1 x + In v1 –…

A: Part d,Given,           lx=tanh-1x+ln1-x2To find : Find the derivative of the given function.

Q: 6. y = In (e* + e*)

A:

Q: 1. Find and simplify the indicated derivative: (a) D: [e¯t sin(2t)]

A:

Q: 3. Find the derivative. sh (a)l= - पक) (a) f(x) = x2 cos x +x tan r (b) h(x) = e" (x² + 4x) %3D t2…

A:

Q: nd the derivative of the following function with respect to x. V5x + 8 V1– 9 cos (4x) Vx² + 10x h…

A:

Q: 2: Find the derivatives of the following function with respect to x. i) x = sin h' y

A:

Q: What is the derivative of y cos e4- 2 7

A: Solution is given below:

Q: Find the derivative of the following with complete solution A. y = sin x - 1 / cos x B. y = x^2 sin…

A: To Find the derivative of the following with complete solution

Q: b) f (x)=(2x-1ifxsI

A:

Q: 1. Calculate the derivatives of the following functions. a) f(x) = In (In(x)) 4x3 b) g(x) =…

A:

Q: Q2/ Find the derivative of each of the following functions:- X 2. log₂ x y = X 1+ tan x 1. y=(sin…

A:

Q: Solve for the derivative of the given functions using the Chain Rule formula. Suppose f(x) =…

A: Given: f(x)=sin(2x)+17 To find: f'π2 and f'(π)

Q: B) Find the derivatives of the following functions: (for only 6) 5) y- In ( sin' 0) 6) y = log:() 7)…

A:

Q: 6. Calculate the derivatives of the following functions. DO NOT simplify the answers! a) g(x)= In…

A: Please refer the attached image for complete solution.

Q: Solve for the derivative of the following functions. Write your answer on a separate sheet of paper.…

A:

Q: 3. Find the derivative of each of the following functions. Justify your answer. (a) f(x)= (b) y e I…

A:

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos…

A: topic- derivative of a function

Q: 1. Find the derivative of the following: (Simplify your final answers.) f(x) = ev3(cos²zx) C.

A:

Q: 6) Find the derivative of the following functions 6.1) a(x) = x²(sin x)(cot x)e" 6.2) b(x) = ()-4

A: To find the derivative of the following functionsFormula:ddx(sin x)=cos xddx(cot x)=-csc2…

Q: What is the relationship between the functions In r and e?

A:

Q: Let f (x) = e10x. %3D Find a formula for the n-th derivative of f, for n 2 1.

A:

Q: Prove each of the following using the definition of the derivative.(a) The First-Power Rule: d/dx  x…

A: Let f is a real valued function. The derivative of f is defined by: f'(x)=limh→0 fx+h-fxh provided…

Q: Here are three functions involving exponential functions: s(x) i) s(x) = 글 (e" -e") i) c(x) = } (e*…

A: Introduction: The trigonometric functions are also differentiable over their principle domain. The…

Q: 5. Given b(x) = (3x – 7)*, if m(x) = 36 (2 tan-1 (1 – 7x)) then m' (x) is %3D %3D

A:

Q: What is the derivative of y log b ( cos? (ax) ? Note that a and b are real numbers. A - 2 a log ble)…

A:

Q: sin(x - y¹) 3+ 2x = sin(x

A:

Q: 4. Find the second derivative for the following function a) )* 22 y3(x+ (an b) f(x)=/2x + at x= 2 c)…

A: See the attachment

Q: FIND THE SECOND DERIVATIVE (y") OF THE FOLLOWING IN ITS SIMPLIFIED FORM (COMPLETE SOLUTION): 2 X = 2…

A: First, evaluate the first derivative dydx (y'). To find y', determine the dxdt and dydt.…

Q: Given the function below: Approximate the following using h = 0.2: f(x) = ex cos(x²) a. First…

A:

Q: h(x) = (cos x)(4x²– 3)

A: Explanation of the answer is as follows

Q: Here are three functions involving exponential functions: i) s(x) = = (e" – e*) $(x) iii) (x) = c(x)…

A:

Q: 13. Find the derivative of the following functions and simplify the answer: 6x+ VE (a) 7x2 – 1 e…

A: As we know that the derivatives of:-  the Quotient Rule:  fg'=f '·g-g'·fg2 Apply the Sum/Difference…

Q: (4) Compute the derivatives of the following functions: (a) f(x) = 4x sin-1r

A:

Q: x2 + 1 Find a formula for the tangent line for y = at x = 1. x + 1 e rational function does not…

A:

Q: Q2/ Find the derivative 1. sin(xy)= of each of the following functions:- 2. y =(Inx)³ 3. y=cos (sin…

A:

Q: Consider the following. Vi+ vT = 5 (a) Find y' by implicit differentiation. y' = (b) Solve the…

A:

Q: 2. Find the derivative of the following functions: -2 (a). f(x) = x² + 4x + 4e" (b). f(x) = 2…

A:

Q: 1. Find the derivative of f(x) = e" (x² – 1)ª. Make any obvious simplifications.

A:

Q: If y = cos x, then the nth derivative of y with respect to x is equal to itself if n is a natural…

A: 9. y =cosx nth derivative and n is divisble by 4  it means n is even number 4,8,12...ny so lets…

Q: Find the natural domain and the derivative of the given function. (a) ln(4x + 2) (b) x · cos x (c)…

A:

Q: g. f(t) = 2t° (sin t)- h. h(x) = - 8 In(4x"

A: Given: (g). f(t)=2t5(sin t)2 (h). h(x)=-8ln4x3

Q: 3. Find the derivatives of each of the following, showing the working and simplifying. (d) h(x) =…

A:

Q: The derivative of the following function at x = 1 y = tan-1V4x3 – 2 is 2 O 0.5 1.4142 O 0.707

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

Q: 1. Find the derivatives of the following functions: a. g(x) = x ÷ sin(x). 2. Find the derivative…

A: Find the derivatives of the following functions:  a. g(x) = x ÷ sin(x). 2. Find the derivative of…

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos*…

A:

Q: Find the derivative of each of the following: (a) (x – 1) sin 2r, - (b) sin 2r T-1 (c) e2" sin 3x…

A:

Q: Answer the following questions for the function k(x) = x³ + x + 1: (a) The derivative at x = - is…

A: The given function is kx=x3+x+1

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: