Differentiate the following functions with respect to x; (a). f(x) = 7x5 + 2loge x – 8e2x + 20x – 5 (b). g(x) = (18x4 – ex)(2 – 3x7)   (c). h(x) = ln x + 6x – 4 – 10                        (d). y =  9x3 – 15x

Q: 1 Find the derivative of f(x) = V7+4x2 - 5.x2 +9

A: we apply chain rule in the first part and division rule in the second part

Q: Find the derivative of the function G(x) 1 + 2x3 – x2 + 5.3x + /10.

A: GIVEN:   G(x) = 12x4 + 2x3 - x2 + 5.3x + 10

Q: 2) Find the derivative of each function f(x) = Vx + 5x+6 %3D а) b) f (x) = 6x'(5x² +3x)10

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Q: Find the derivative of the function f(x) = (5x^4)/12

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Q: Find the derivative of the function.

A: fx=x3-2x+3x-3

Q: 1. Find the derivative. (a) f(x) = (6x² – 8x + 4)4 2х -5 (b). у %3D 2x2 - 10

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Q: Find the derivative of f(x) = -4x ( 3' *(3"). %D 3+4

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Q: Find the derivative of f (x) = x2 + 2x + 2.

A: The given function is, fx=x2+2x+2 To find the derivative of the function, we use the power rule of…

Q: The derivative of f(x) 4 (x2 + 3x) is O -4x3 (2x + 3) -4x 2(2x + 3) 4 O 4a-2(2x + 3) 4.x + 12

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Q: Find the derivative of the function. g(x) = √(4 − 3x2 )

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Q: Find the second derivative of the function. f(x) = 5(2 − 7x)ª

A: The given function is fx=52-7x4. Find the second derivative of the given function. Here we use the…

Q: In(6x) Given f(x) the derivative f'(x) is 1 6x 1 6x ,6x 1 6

A: Topic-Derivative

Q: Find the second derivative of the functionf(x) 3Vx+2 2x+1

A: Given

Q: Find the second derivative of the function.

A: Given function is  fx=4x32 The derivative used here is  dxndx=nxn-1 The derivative of the first…

Q: Find the derivative of the function.    t(x) = (x2 − 8x3)/(x)

A: Given, t(x)=x2-8x3xTake 'x' common from numerator,we gett(x)=xx-8x2xCancel 'x' from both numerator…

Q: Find the derivative of the function. g (x) = 6x-3 + 2x Og (x) = 18x + 10x-6 %3D Og (x) = -18x-3…

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Q: Let L(x) be the linearization of the cube root function at x=8. When using L(x) to approximate the…

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Q: Find the local and absolute extremum for the functions over their domain: 5. f(x) = vx2 + 8x + 20

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Q: For the function f(x) = (5x² − 2)4 determine the second derivative in factored form.

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Q: Find the 3rd derivative of the functions: y = 12(5x2 –1)(x2 –1)

A: Find the 3rd derivative of the functions: Given y=12(5x2-1)(x2-1) To find dydx, d2ydx2, d3ydx3

Q: Find the derivative of h(x) = x 2(9x + 2).

A:

Q: Find the derivative of the function.

A: the given function is: hx=ln2x2+1 we have to find the derivative of the given function.

Q: Find the absolute maximum and minimum, if either exists, for f(x) = x - 8x + 9. Find the first…

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Q: What is the derivative of p(x)=(2x^4+2)^x

A: Using logarithmic differentiation we can find the derivative of the given function.

Q: Consider the following. f(x) = 5x2 + 4x – 18 (a) Find the derivative, by using the definition. f'(x)…

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Q: Find the second derivative for the function f (x) = 4e . 1 - 2x3

A: Given: fx=4ex-12x3 for finding second derivative of given, we find first derivative then find…

Q: Find the derivative of f (x) = e(x3 − 10x2 + 8 ) .

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the derivative of f(x)= x^4+3x^3+7x^2+15x+31

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Q: Find the third derivative of the function f(x)=2x^(5)-6x^(4)+7x^2-9x+20

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Q: f(x) = x^3 -1000x +2022 How many local minima does this function have? are inflection points of…

A: Given function f(x)=x3-1000x+2022

Q: 1 y = 8x* + 7x³ + =x² – 14x + 6 %3D -

A:

Q: Find the global extrema of the function f(x)=x4−2x2−1 on [0,+∞).

A: Given function is Differentiating both sides with respect to x, we get Now, we will find critical…

Q: Find the derivative of the function. f(x) = (3x + 2)3(x2 + x)2

A: Differentiation use product formula

Q: The higher derivative of y = 5x³ – 2x is O 15x2 – 2 О 30 O 30x

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Q: V/2x+3) (x²+1)" 17. f(x)=-

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Q: Find the derivative for f (x) = V4 + e2x a. e2x /4+ e2x b. 1 2v2e2x xe2x-1 /4+ e2x C.

A: To find the derivative of fx=4+e2x.

Q: Find the derivative of the function. f(x) = (x3 + 7x + 5)(3 +1/x2)

A: To determine: Find the derivative of the function.

Q: Find the derivative of g(x) = 4x 1+4* •

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Q: Find the derivative of the function f ( x ) = x2−10x+3 using First Principles.

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Q: Find the derivative of the function. f(x)=(x^3+9x+8)(7+1/x^2)

A: fx=x3+9x+87+1x2⇒fx=x3+9x+87+x-2

Q: Find the derivative of the function. p(x) = - 12x 2. +4x %3D p'(x) = 2/3

A: We have to find derivative

Q: What is the first derivative of p(æ) = In (4x3 + x² +1)?

A: Given function is p(x)=ln4x3+x2+1

Q: For k(x)=(−3x2+2x−3)(x−2)(−x+3), find the derivative of k(x) using the product rule.

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Q: The derivative of f(x) = x4 + 4e2x is-

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Q: Find the local and absolute extremum for the functions over their domain: 2. f(x) = x3 + 4x2 – 11x –…

A: Given function is  f(x)=x3+4x2-11x-2

Q: Differentiate the function ln(x2+y2)+2arctan y/x=0 implicitly.

A:

Q: Suppose ƒ is an even function and Evaluate

A: Given f is an even function, ∫-88f(x)dx=18

Q: (4) Find the derivative of h(x) = 5x³esec(x) .3 %D

A: We need to find the derivative of

Q: 1. Find the derivative of the following. f(x)=13x* -7x²+5x²+11x+75 a.

A: Formulas:ddx(a f(x))=a ddxf(x)ddx(xn)=an xn-1ddx(a)=0;  where a is a…