Which of the following pair of functions is linearly independent? (a) e3*, e(x-3) (b) 4, sin?x + cos?x (c) 2sin2x, sinxcosx (d) sinhx, (e* – e-*)

Q: The derivative of the function y = (10e* – 10x*)(tan x) is: a. y' = (e* – 40x3) tan x + (10e* –…

A:

Q: What is the derivative of y= 3Arcsin xº, 3 Arcsin x In 3 A y' = 1 - xa 3 Arcsin x* In 3 3 B y' : (а…

A:

Q: Evaluate the derivative of y = cos '2x - In 1-4x, where x = 0.125 -12> 2

A:

Q: Compute the following derivatives using the chain rule. g(y) = ln(1 + y).

A: Take 1+y = t  And use chain rule

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. G(x) =…

A:

Q: Find the derivatives of the functions in Exercises s = cos^4 (1 - 2t)

A: The given function is s=cos4 1-2t. Obtain the derivative as follows.

Q: 15. Which of the following has terminating derivative? 1 1. у %3 Зх3 — 2x2 + х-1 —5 II. y Зx+2 1 . у…

A: We will find the terminating derivative.

Q: Find the third order derivative of y = In(cos(2x))³. A. y' = -40sec² (2x)tan(2x) B. y' = -80sec?…

A:

Q: Find the derivative of f(x) = log, (x° + x – 1). %3D 2 + x - 1 f (2) = %3D (3z* + 1) (In 2) (3z +1)…

A: Given:     fx=log2x3+x-1

Q: у (4) %— Зх3 8 e x7

A:

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: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction ef 4i - 3i

A: The directional derivative of a function f(x, y) in the direction of the unit vector (a, b) is given…

Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: Given function is y=sin4 cosz. To find the derivative of the given functions. Solution: Chain rule…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. G(x) =…

A:

Q: Find the anti-derivative of g(x) = sec(x) tan(x) which contains the point (TT, 0). O G(x) = -csc(x)…

A: Solution to the anti-derivative can be found by integrating the function.

Q: estion 9 Find the derivative of f(z) = 3z13 - 4+1. IDo? la sin (a) f' (x) =}

A:

Q: respect to x of/ /(3Vi-1) dt is 3x – 1 by the 2nd fundamental theorem of C The derivative with (A)…

A:

Q: Find the derivative of Screen Shot 2021-10-05 at 7.41.38 AM.png ... In sin-1 e y リ= 2 1 ® y' = -x )…

A: We can solve the problem by just doing the derivative of the function

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

A: singx

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 1-x (x+ 3)5 15) у - In 6х- 8 A)…

A: Given that:y=ln1-xx+35To find derivative

Q: If f(x) = Α) B C D tanx sec ³x 1 + e tanx 1+tan²x 1+ e tanx sec²x 1+1² 1+e' -dt, then f'(x) equals…

A: We have to find derivative of given integral.

Q: Which of the following shows how to find the derivative of f(x)? 3e* f(x) |3D ex-7 (ae(*-7) -…

A:

Q: Calculate the derivative e12x d In (t)dt dx using Part 2 of the Fundamental Theorem of Calculus.…

A:

Q: OFind the derivative of the 1 +5 (a). f(z) = %3D T2-5

A: As per the guidelines we can solve only one question at a time so if you need more answers then…

Q: Let f (x) =x. cos(x2). what is the correct result of the derivative of f with respect to x? A…

A:

Q: Find the derivatives of the functions in Exercis

A:

Q: Compute the derivatives of the given functions. f(2) = In (7z²). 7a?). f'(x): / (z) = help…

A:

Q: f(x) = 2x² cos(r®)

A: Given Data: Function: f(x) = 2x2 cos(x5)   The product rule of differentiation is,

Q: 2. Find the derivative of each of the following: (a) f(x)= 3" cos² (}x) %3D (b) h(x) = Vrd – 4x + 1…

A: (a) Consider the given function, fx=3xcos212x Here the objective is to find the derivative of the…

Q: 1. Find the derivative of each of the following functions a) f(x) = cos5x %3D b) g(x) = cos 5x c)…

A:

Q: Use the chain rule to find the derivatives of f(x) and g(x) as well as f'(0) and g'(0): f(x) = (2x³…

A: According tp our guidelines we can solve only one question so we are solving 2nd question for you.…

Q: 3. Calculate the derivative of f(x) = tan(4t) dt. %3D -1/16

A:

Q: Find the derivative of h(x) = cos (2x3 - 5). %3D Provide your answer below: W(x)= O %3D

A: We will find the derivative of h(x) in the following step.

Q: 8. Find the derivative of the f(x) = ntan x at x = " А. п B. 2 In(1) C. π In (π) D. 2 n In() E. 2n…

A:

Q: Calculate the derivative e8x d In (t)dt dæ using Part 2 of the Fundamental Theorem of Calculus.…

A: Given To apply the fundamental theorem of calculus first simplify these integrals so that this…

Q: Evaluate the implicit function by finding dy/dx of x³+3y=3xy

A:

Q: Apply the first derivative test to indentify all relative extrema. (b) f(x)=x²-2+1 (c) f(x) = cos²…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Find the derivative of the function. 92-4x + h(x)= e 18x – 4x2 –1 92-4z++ x2 O b. 9x - 8x² – 1…

A:

Q: Consider y = (1 + 3x²) Arctan x - 3. what is its derivative? %3D 1 +3x2 1 + x2 A - 6x Arctan x 1…

A: 7). As we know that: The product rule:  f·g'=f'·g+f·g' The sum/difference rule: f±g'=f'±g' The Power…

Q: 4.) Consider the function g defined by g(x, y) = car ( 7X Jj ) + logg(x-y) does 9 have the maximum…

A: Given: gx,y=cosπxy+1log3x-y

Q: d) Hence form a conjecture for the derivative of functions in the form y = (ax + b)². e) Prove your…

A: As you have mentioned I am answering Question (d) and Question (e)

Q: 29. Prove the following derivatives by using the definition of derivative. (a) (") = n. dx nxn-1

A: topic - derivative and limits

Q: Find derivative of each; A) m(t)= In(4t^3+tan(5t)) B) h(x)= 4sin^8(5x+1)

A:

Q: y' – ey : = sin x

A: In this question, we have given a differential equation y'-ey=sin(x) here, we need to check either…

Q: Find the third order derivative of y = In(cos(2x))". A. y' = -40sec²(2x)tan(2x) B. y' = -80sec…

A:

Q: Find the third order derivative of y = In(cos(2x))5. %3D A. y' = -40sec² (2x)tan(2x) %3D В. у' 3…

A:

Q: 4. Find the second-order derivative of the following function: f(z) = log, cos z + In %3D

A:

Q: (3) Compute the derivative of the function Cos tdt.

A:

Q: Compute the derivative of the given function. f (x) 10x-1/4 cos e + 7 sin a %3D -

A:

Q: Find the linearizationsof the following functions at x = 0. tan x

A: Linearization is tangent line at a point x=atangent equationy-y0=mx-x0m=f'a