Determine the following a) f(r² -x=1)dx

Q: Show that is C is a function of x with derivative C'=C/x and N=C/x, the d/dx (C/x)=(C'-B)/x

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Q: ind the derivative of the function f(z) = (2r+7) 71+11 %3|

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Q: Use the Quotient Rule to compute the following: d t²+ dt \ t2 The derivative is:

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Q: Compute the second order derivative f"(x) for f(x) = 3x* -/x. %3D 36x2- 4x2 Ob.36x2 + 3/2 3/2 1 OC.…

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Q: f(x) = xe (1+e*)

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Q: What is the derivative of f(x) = Select the correct answer below: O 4V/2 O 2012 3 O w/s O 16V/2 о 3…

A: Derivative of function f(x)=43x54 at x=4

Q: Find F'(x) given that F(x) = sin (t2) dt

A: Derivative of integration

Q: Which among the choices has the first derivative that is e (2x+1) (x +3) ? Of(띠) 3D + 글z2 + 2x-8 O…

A: given function has first derivative is f'x=2x+1x+3    f'x    =2x2+7x+3

Q: Compute the derivative: d 4 dx x2 5 x=1 The derivative is:

A: The solution of the problem is given in the next step.

Q: Calculate the following derivative if f(x) = 6x° – 2x?. daf %3D dx4 x=1 II

A: ddxxn=n xn-1

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

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Q: Use the Power Rule to compute the derivative.

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Q: Find the (a) derivative y'= dy dx y = (n² + 5 secx) ㅠ of following Question tog 3 x

A: Note: Due to guidelines i can solve only your first question. Solution: a) y=πe+5sec xlog3x…

Q: I the second derivative of the function F(t) = 7tsin(º). ver F"(1) =

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Q: Compute f dx, where f(x)=|x|.

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Q: Calculate the error of approximation with EA for the following functions Fix) = In 3x. when x = 4…

A: EA = 0.0030056

Q: 4. Find dx/dy of the following functions using inverse functions rule. (a) f(x) = (b) f(x) =

A: a fx=xx-3y=xx-3using inverse function rulex=yy-3dxdy=ddyy12y12-3u=y12            v=y12-3dudy=12y-12…

Q: d Find the value of f(x) if f(x) : cos (t) dt. dx. COS f(x) =

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Q: What is the value of f (5) if f (t) sin (Ta) dt :? 1

A: Given, ∫1xfttdt = sinπxx   We have to find the value of f5

Q: of dx- = 0, then dy |=0. Prove that is a function f is harmonic

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Q: Suppose f(x) = | sin(t?) dt. Find f'(x). x2

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Q: dx a(1+x?)

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Q: Find the derivative (dy/dx) of the following functions: h) у%3D Зx7 —7х3 + 21x2 - i) y = (x² +…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

Q: Q5: Find dx for the following functions: (3) y = ex.sin² x In√x

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

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Q: Find the following derivative of f (x)= 2x³ 4x4 + 6x. a ab Va |a| sin (a) f(6) (x) =

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Q: Differentiate the following function. y = x12 ex dy dx II

A: To differentiate the function y = x12ex

Q: Differentiate the following function. y =x³ ex dy dx II

A: Our Aim is to differentiate the following function given below:-y=x3ex -(i)

Q: Compute f dx, where f(x)= |x|

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Q: Given that f(x) = 5x° + x³ + 2, find the derivative of f- by using dy che formula d.x 1 Check dx…

A: To find: The derivative of inverse of f(x)=5x5+x3+2 by the formula dydx=1dxdy. Calculation: Find the…

Q: Find the third derivative of f(1)= 2x(x -1)" Oa 18 b.14cos 13 OC16sim Od12

A: we all know that dxndx= nxn-1. and first derivative dfxdx=f'x and second derivative df'xdx=f''x and…

Q: Which of the following has a derivative of * dy = 32.x + 24? dx

A: The derivative dydx is given by dydx = 32x + 24                          ........(1)

Q: 6. y = In (e* + e") 7. y = tan e + etanax 8. y = In(x + Vř +1) 9 y = Arctan(;

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Q: Use the rule for recipocals : f '(x) f?(x) d 1 dx [ f(x) to find the following derivatives…

A: Given: Reciprocal Rule: ddx1f(x)=−f'(x)f2(x) Find: 1)  ddx1x2+2x+1=?2)  ddx1sinx+ex=?3)  ddxπx+1=?

Q: Evaluate dy for f(x)= (square root of x) +3 where x=9 and dx=0.12

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Q: Given that f(x) = 9x + x³ + 6, find the derivative of f- by using dy the formula dx 1 Check your…

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Q: ,dy QI/ Find (- ) to the following functions: dx

A: We have to differentiate with respect to x.

Q: Find f(2x)dx if f(x)dx = 1. Enter the exact answer. f(2x)dx

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Q: –1 dx

A: Solve the following

Q: Use the Quotient Rule to compute the following: d t2 +1 dt t2 – 1 The derivative is:

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Q: Find the derivative(dy/dx) of following function f(x) = Sin(2x) (x+1)? %3D

A: It is derivative problem.

Q: 8.What is the derivative with respect to a of f(x) = (5 – x2)²? оА. (5 — а?) (5 — а*) O B. 2(5 – a?)…

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Q: Evaluate the second derivative of e22.1.png ... acos(byx) f(x) x2 if a = 165 and b = 0.3 at x = 3…

A: Follow step 2nd and 3rd.

Q: If f(x) • g(x) is to be integrated with respect to x, taking dx as the differentiated variable,…

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Q: Compute the derivative of the following function. f(x) = 2 e 2x f'(x) =L %3D

A: To find the derivative

Q: Consider the function f(x) whose second derivative is f"(r) = 5x +5 sin(r). If f(0) = 4 and f'(0) =…

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Q: 4. Take the following derivatives; a. f(x) = x"Inx b. y = sinx 3 C. g(t) = Vx - 4

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Q: Consider the following function: y = x*. dy dz ||

A: The given function is y=xx2. Rewrite the given function as follows. y=xx2y=elnxx2y=ex2 lnx

Q: Show that, for a function f(x) with anti-derivative F(x), d s)ds f(x). %3D dx a

A: Suppose f(x) has an anti-derivate F(x), v(x) and u(x) are differentiable, then Leibniz's rule of…

Q: a) Differentiate y = with respect to x. Hence, evaluate 5x+1 4 J. (5x + 1)2 dx

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