Let f (x) =x. cos(x2). what is the correct result of the derivative of f with respect to x? A s'(x)=cos(x²) – 2r?sin(x²) = cos(x B f'(x)=2x2sin(x2) + cos(x²) ©s'(x)=cos(x²) – xsin(x²) Os(x) = - 2v²sin(x²?)

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A: As we know that: The Power rule: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2 Given: fx=2cosxx+1

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Q: Find the third order derivative of y = In(cos(2x))³. A. y' = -40sec² (2x)tan(2x) B. y' = -80sec?…

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Q: Which is the derivative of y= sin (x2-2x + 1)? (2х -2) (2x-2)Cos(x²-2x + 1)

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A: We will prove the given statement.

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A: Given: the function xfx, where f is a differentiable function of x.

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A: To find dydx, rewrite the equation and then differentiate with respect to x.…

Q: Find sixth order derivative of the function f(x)=(x-5)^7.cos(5x) by using Leibnitz theorem.

A: n! = n × (n-1) × (n-2) × (n-3) × (n-4) × ............ × 1

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A: singx

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A: We will find the derivative of y with respect to x as following.

Q: find the derivative of y with respect to the appropriatevariable. = cosh-1 2√x + 1

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Q: 1) Find the derivative of f(x) = 1+sin 2x %3D 2 cos3 x

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A: Solve the following

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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: find the derivative of y with respect to x, t, or θ, as appropriate. y = x4/4 ln x - x4/16

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Q: Find the derivative of y with respect to x. 1, 1+x2 In 1- x3 y

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A: Given : y=lntan-19x5

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Q: Calculate the derivative of the following function. y= sin (cos (3x)) If the Chain Rule only needs…

A: In the question we have to find derivative of the given function.

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Q: find the derivative of y with respect to x, t, or θ, as appropriate. y= θ(sin (ln θ) + cos (ln θ))

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Q: (a) Find the first derivative of the function y= la) with respect to x by using the chain rule.

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Q: Find sixth order derivative of the function f(x) = (x – 5)7.cos(5x) by using %3D Leibnitz theorem.

A: If y=uv where, u and v are functions of x then un and vn denote the nth derivative of u and v with…

Q: find the derivative of y with respect to x, t, or θ, as appropriate.

A: On simplification, we get

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Q: Find the first derivative of g(x) = 2 In(x)tan(x*). g'(æ) = %3D

A: Given that g(x) = 2ln(x) tan(x^4). Find first derivative of this function. We know that derivative…

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A: Differentiate the given function implicitly as follows.