Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) fx) = 6x - 4x* - x² F(x) =

Q: Find the derivative of each function e 2x a. f(x) = 2x+1 b. f(x) = In Vx + 2x c. f(x)= x²e* – 6x

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Q: Find dx2 by implicit differentiation, given x³ + y³ = 8. d?y dx2

A: Given that, We have to find the value of  For that simply follow the step given as below

Q: Find the derivative of the function 1 4. y= 4x +8x dy

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Q: Find the derivative of the given function by definition 6" y 5xar+1 + 3r

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Q: Find the derivative of the function. f(x) = V 5x + 4

A: Question number 1,Given,          fx=5x+4

Q: Find the first derivative of y with respect to x (y') of the given function using rules for…

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Q: What is the derivative of f(x) = x² +x² a +2 where a is a constant ? xa+2

A: We write f(x) using exponents f(x)=x7+x2+a+2xa+2f(x)=x7+x2+(a+2)x-(a+2)

Q: Find y" by implicit differentiation. 3x3 + 5y3 = 7 y" II

A: Given       3x3+5y3=7   1using implicit differentiation, w.r.t x1  ddx(3x3) +ddx(5y3)=ddx(7)…

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: Find y" by implicit differentiation. x2 + 9y2 = 9 y" =

A: Here we have to find the both y' and y"

Q: Find the derivative of the function. 4x +6 y-D y'3D

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Q: find the derivative of the function y=-5(8x^2+7)^-6 dy/dx=___?

A: Given function is :  y = -5(8x2 + 7)-6

Q: Find the derivative of the given function. y= 2x°-8x +16x+4 dx II

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Q: Find the derivative of the function. 4 y = 3x3 - 13x - x6 dy dx

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Q: Find the derivative of the function g(x) g'(x) = ex + 3xe (2+3x)² = x| X et 2 + 3x

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Q: Find the derivative of f(x) = 8e7x +e=x? f'(x) =

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Q: Find the derivative of the given function. y= 2x- 13x +35x +5 dy 口 dx %3D

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Q: Find by implicit differentiation. dx 1. x3 - xy + y2 = 7

A: topic - implicit derivative note - As per bartleby guidelines, we are supposed to answer only first…

Q: Use the alternative form of the derivative to find the derivative at x = c  (if it exists). f(x) =…

A: Definition used -           Alternative form of derivative -…

Q: Find xp by implicit differentiation. S 4e*"y = 2x

A: According to the given information, it is required to find the implicit differentiation.

Q: *(x) = x² +x – 7 , find f'(a) at a = -2 by using the definition of derivative.

A: To find the f'(a) using definition of derivative

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. g(x) = 2x2…

A: Given function is gx=2x2-3x. We know that, f'x=limx→cfx-fcx-c Using the above formula of derivative,…

Q: Find the derivative of the function. 7x 7x flu) du J3x 0 fu) 3x d du g(x) Hint: fu) 3x u5 g'(x)

A: To determine the derivative of the function.

Q: suppose that x and y are related by the given equation and use implicit differentiation to determine…

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Q: Find the antiderivative of x/sqrt (x2+1) and verify it by differentiation?

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Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. f(x) = x3…

A: Given: fx=x3+2x2+1 , c=-2 To determine: Derivative of given function at x=c

Q: Find the third derivative of the function: Y = =+ VX3 %3D

A: To find the third derivative of the function: y=1x+x3

Q: Find the derivative of the given function. y = - 9sin (5x4 - 6) dx ||

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Q: Find the derivative of y with respect to x if y = (12x - 24x + 24) e - 3x. y' =D %3D

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

Q: Find the derivative of the function. y=-6(8x+8)-6 dy/dx=

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Q: by implicit differentiation if x² +9x+9xy-y² =16 Find x dy

A: Find dydx by implicit differentiation if x2+9x+9xy-y2=16. Solution: Power rule of differentiation…

Q: Find the derivative of the function using the Power Rule for Functions. y = (x² + 6)²(4x³ – 1)3 dy…

A: Y'= ?

Q: V3x – y+ 6a*y? = 9y

A: Given: 3x-y3+6x4y2=9y

Q: Find the second derivative of the function (r² + 1)(x² _ z +1) U =

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Q: What is the anti-derivative of q(x) = 2e+5 3x 3 ? (Do not include the constant C in your answer.)

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Q: Ax) = Vã Vx = /x хх e

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Q: Find the given flx), + 2x derivative of function. %3D a+x

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Q: Find dx by implicit differentiation for the function x* + x³y3 + y7 = 8

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Q: Use the rule of differentiation to find the derivative of the given functions 1. y = (4x – 1)5 2.…

A: 1. y=(4x-1)5, Taking derivative with respect to x, ⇒dydx=5(4x-1)4×ddx(4x-1)         =5(4x-1)4×4…

Q: Find the derivative of the given function y = (2x+ 5)v4x – 1

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Q: y= 4x2-2x - 3

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Q: Find the derivative of the function. y= -3(6x2 +8) -6 dy dx (Type an expression using x as the…

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Q: Find the first and second derivatives of the function.

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Q: Find the derivative of the function. -Vx? y = + 36 6 + Vx2 + 36 1 In 36 6x2

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Q: V(7x – 7y)³ – 2y? = 8x

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Q: Find y' by direct differentiation (with respect to x). y = (5x2 + 6x − 7) ln x   and  y = (e-x)/…

A: Solution -a.)Given function -y = 5x2+6x-7lnxDifferentiating on both sides with respext to x,dydx =…

Q: Use the definition of the derivative to find df/dx. f(x) = x/(1-3x)

A: Given, function

Q: Find the derivative of the function: f(x) = Vx + Vx + 1 1 +

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Q: Find the derivative of the function. 4x° +8 y = y' =O

A: We have to find