dy Compute the derivative y = . %3D y = 7x – x-4 (Express numbers in exact form. Use symbolic notation and fractions where needed.) y %3D

Q: Find the derivative: h(x)= [ dz a. b. x+1 2+2 C. d. 20+1) e. None of the above.

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Q: Find the derivative df/dk. " f (k) = ek + a*

A: Find the derivative of the given function.

Q: Find dy without using the quotient rule; rather, rewrite the function by using            dx     a…

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Q: Find the indicated derivative or integral a. D, (3** * ) c. D, log,, (x³ +9) –3x а. D, b. |x 2* dx…

A: We know that Dx ax = ax·ln(a) Dx af(x) = af(x)·ln(a)·f'(x)   ∫ax dx = axln(a)+C   Dx loga x =…

Q: ind the derivative of the function: y=2e^x cosx

A: Here use multiplication rule in derivative

Q: dy Find using implicit differentiation, for the equation æ4 + yt = 7 is dæ O O O

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Q: Find the derivative of y with respect to x. y = In 6x? 12 O A. 2x В. x + 6 Oc. OD. 2x +6

A: The given function is- y=ln6x2 Differentiating y w.r.t. x- dydx=16x2×d6x2dx

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: Solve for the following implicit derivative: d²y si sen(y) = ycos(2x) dx?

A: We have to find the double derivative of the given function.

Q: Find derivative of the following functions: i. In(x*sinh x) ii. y = csc e* 7x

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Q: Let y= 9 x5 – 1. Find A, B, and C so that dY = AxB + C. A В C = Then find the value of the…

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Q: xy2 + x tan y = y sin b. ye* + sin xy = x tan xy a.

A: a)To determine the derivative of the function given by; xy2+xtan(y)=y sin(x)  Differentiate both…

Q: Suppose y=4V X +6V x. What is the value of its derivative at a=64? Write the answer in exact form,…

A: The function is given by y = 4x+6x3 To evaluate: The value of dydx at a =64

Q: Find dy /dx for the following function: y = Inln2!nx

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Q: ind the derivative of the function y = (x+ 8 sinx) (1+ 14x), and simplify the answe

A: Given : y =(x+8sin-1x ) ( 1+14x)

Q: Compute the given derivative. dx x=-9 e 1/9 O 9e9

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Q: Calculate the derivative a 1 y = x + 3 (Use symbolic notation and fractions where needed.) dy dx x-4

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Q: What is the value of the derivative of y=sin(x)cos(x) when a = 2? Write the answer in exact form, an…

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Q: Find the first derivative for each tunction. O fex) =3x"(ax^-1) O g4) = (t+)(t? -t +i) 3.

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Q: Calculate the derivative. (Use symbolic notation and fractions where needed.) d (3r° – 21) dt = dx…

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Q: Find the indicated derivative. dp for p = 1 - () 4q dp P. %3D

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Q: d?y Find by implicit differentiation when dx? 5xy – y? = 9

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Q: dy Find using implicit differentiation, for the equation a + y=8 is da O O

A: Differentiate both sides with respect to x.

Q: Find the derivative of the following function. -3 y = (3x* + 4)* dy dx

A: Given a function  y=-3(3x4+4)5 To find the derivative dydx of the function.

Q: Find the second derivative, d'y where y is related to a implicitly by the equation below. 3a + 2y =…

A: the equation of given implicit function is: 3x3+2y3=12 we have to find the second derivative d2ydx2.

Q: Find derivative of the following function. -8x 8X + e y%3= dy dx I3D

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Q: Calculate the derivative of the following function. y=e*(4x- 9)5 dy dx

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Q: Find the indicated derivative. dy if y %3D - 3х xp dy dx %3D

A: Recall: dα f(x)dx=α d[f(x)]dx; where, 'α' is any constant. dxndx=n.xn-1

Q: (væ) + log, (5x² – 3) + ex² Find the derivative of y = arc tan

A: Explanation of the solution is given below...

Q: Find the derivative. y = In /x+5 y' =D

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Q: dy da Find the derivative of the function x° In 3y = y sin 3x + e5 x %3D Answer:

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Q: Find the second derivative of the given function. y= 4x+9x %3D dx

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Q: 3x Write down the derivative of the function V3+ cos? (x) dxc.

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Q: b.y = x100 ; find dx100 d'100y (100th derivatives)

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Q: d'y Use implicit differentiation to find dx? if 3x? - 2y = 3. dy dr2

A: Topic:- application of derivatives

Q: x-1 dy 6. y = ( ). \x+1 dx

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Q: d'y 6. Find by implicit differentiation. x + y = sin y

A: It is implicit differenriation.

Q: Calculate the following derivative. (Use symbolic notation and fractions where needed.) d (15 Vsin…

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Q: ind the second derivative in its simplified form 5. x= 1/t-1 , y= t/t^2 -1

A: Given :  x=1t−1  and  y=tt2−1

Q: - 7x Find the derivative of the function y =e sin 3x.

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Q: Find the derivative of the function. sin(x) y = In(1 + 7v) dv g'(x) = Jcos(x)

A: Solution

Q: Find dy/dx by implicit differentiation. x6+y7=45

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Q: Find dy/dx by implicit differentiation.   x^2+11xy+y^2=12

A: Find dydxddxx2+ddx11xy+ddxy2=ddx12ddxuv=vdudx+udvdx…

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below y= 3 (Arccos…

A: Given function, y=3cos-1(2x)x(lnx)

Q: Find dy/dx for the following function:: √y-etanx = 2

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Q: Find dy/dx by implicit differentiation for the following.:x2ey + y = x3

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Q: t3 – 3t? + 5t dt Find the general anti-derivative:

A: The solution as follows :-

Q: dy if 20 – 3y? = 4. dæ? Use implicit differentiation to find - d'y

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Q: Find dy/dx by implicit differentiation and evaluate the derivative at the given point. xy = 24,…

A: Product Rule: ddxu.v = dudx.v+u.dvdx w.r.t means with respect to

Q: d (2a*e" + 4a*) dx Calculate the derivative:

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