sen(x Jcos(r) In(1+2v)dv

Q: f(x) = acos(b\x) x2 COS

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Q: 2. Compute the derivative of the following functions: 1-e-* (a) f(x) = V1 – sin³ x, (b) f(x) =

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Q: Compute the derivative of the function F (x) = L evi dt.

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Q: Find the derivative of function.

A: The given function is f(x) = ln(xex+2).We have to find the derivative of this function with respect…

Q: What is the derivative of 1+x3 at the point (1, )? O 1/4 O- 1/4 O 1

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Q: Find the derivative of the function. 5x g(x) = [¨ cos(r}]dt cosx

A: We will use Lebnitz rule to differentiate the function .

Q: Find the derivative of the function.

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Q: Compute the derivative of f(x) = 7 ln (x + 10) + In (x³ ): Answer: f'(x) =

A: Given function is  f(x)= 7ln(x+10) + ln(x3), we have to find the derivative of f(x) with respect to…

Q: What is the first derivative of s(x) = 4e.

A: Given function - s(x) = 4ex-3Differentiating on both sides with respect to x - ddxs(x) =…

Q: compute the derivative f (x) = ln(4x2 + 1)

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Q: f(x) = cos (x – a -2).

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Q: Find fifth order derivative of the function f(x) = x*Sin (2x +1) by using Leibnitz theorem.

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Q: Find the derivative of the function. f(x) = V4 +x sin x 4+x sin x = dx

A: Derivative of the function is given below

Q: Use forward-difference formula to evaluate the first derivative of y = sin(x) at x = O 2√2 π -2√2 ㅠ…

A: Given that y=sinx. We have to find the first derivative of y=sinx at x=π2 using a value of h=π4 by…

Q: Find the derivative of the function. rsin(x) In(2 + 9v) dv Jcos(x) y'(x) =

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Q: Find the derivative of the function.

A: Given: y=lncosxcosx-1

Q: Find the derivative of the function. 3x2 g(x) • dt 4 + t3 tan x g'(x) =

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Q: p(x) = In(x)^/x

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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 function.

A: To fFnd:  Derivative of y=ln 4ln3x

Q: Find the derivative of f(x) = -1 csc (cos r)

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Q: Find the derivative of z=(ln5)e^x dz/dx=

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Q: Use three-point midpoint formula to evaluate the first derivative of y = cos(x) at x =; using a…

A: The three-point midpoint rule to calculate f'(x) is f'(x)≈f(x+h)-f(x-h)2h, where h is the step size.

Q: · f(x) = sin(In r²) %3D

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Q: 5. Find the first order derivative with respect to y of the function U = In/x² + y² + z²

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Q: Compute the derivative of f (x) = (x – 3r) cos(r). -

A: You will find the derivative of the given function using the product rule of differentiation which…

Q: Find the derivative of h(x) = In 25

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Q: Find the derivative of the function: f(x) = [sin(4x + x)] [cos(x4 + 4)] f(x) = e3x²+*(cscx + secx)2…

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Q: Find the derivative of the function. 10 f(x) = + 6cos x Vx

A: Differentiate above equation with respect to x

Q: Find the derivative of f(x) = e" – a3 +In(x) - In(x)

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Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = 4, 8'(2) = 5, and g"(2) =…

A: Given: The function singx with g2=π4, g'2=5, and g''2=3, To find: The second derivative of given…

Q: Calculate the derivative of the following function. = (x + 8) (x² - 1))° dy dx

A: By using the following equations we can find the derivative of the given function.

Q: Y= In (In2 (1-x))re?

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Q: Find the derivative of the function. sin(x) y = /cos(x) In(8 + 3v) dv y'(x) = 0

A: Here we use Leibniz integral rule and define the formula:

Q: Find the derivative. 8 + e y = In 8 + et 8 - ex.

A: Given,          y=ln8+ex8-ex

Q: Find the derivative of h(x) = (1+ cos x)*

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Q: Find the derivative of the function. *sin(x) y = Jcos(x) In(6 + 3v) g'(x) =

A: use Lebniz's Rule:   d/dx ∫[a(x),b(x)] f(t) dt =f(b(x))b' - f(a(x))a' Here, a(x) = cos(x) b(x) =…

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

A: topic - derivative and limits

Q: 8x+9 In(, x3 dx

A: Here we will sove derivative of given function,

Q: Find the derivative of both a and b a. x csc-1(1/x) b.(esin2x)/[In(cos2x)]2

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Q: 1. Find the first order derivative of u = x*.

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Q: (x² +SJ° In 14-X つ. dr

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Q: Find the derivative of the function. 5/1 x+1 In 22 + arctan x %3D X -1· dy dx

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Q: Find the derivative of g(x) = fecost dt.

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Q: Find the derivative of y with respect to x. 6x + 7 -1 6. y3-Cos %3D

A: dydx=?

Q: Compute the second derivative with respect to r of 3x + 8 y = at x = 1.

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Q: 8. Find the derivative of y = In(3t) dt.

A: To Determine: Find the derivative of given integral:…

Q: Find the derivative of V(x) = ln(sin x) – (x4 – 3x)10

A: We can find the derivative as below.

Q: What is the derivative of the function h(x) = ((4x^2-4)/(cos(x)))^8

A: We have to find the derivative of ((4x^2-4)/(cos(x)))^8 = 4^8(x^2-1) sec^8(x)= 65536(x^2-1)sec^8(x)