Let f(x) =x-cos(x²). what is the correct result of the derivative of f with respect to x? A f'(x) =cos(x?)– 21?sin(x²) B f'(x) = 2x²sin(x?) + cos( © F(x) =cos(x?) – xsin(x²) = cos(x - D(x)=-2x²sin(x²)

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A: Given 1. y=sin-1(2x2)2. y=tan-1(2x25)

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Q: 2. Find the derivatives of Y with respect to x if; x=arc sin ex.

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Q: Find the derivative of the function. rsin(x) y = In(1 + 5v) dv y'(x) = sin x In(1+5 cos x) + cos x…

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Q: compute the derivative y = sin(2x) cos2 x

A: Given y=sin(2x)cos2x The product rule of derivative is given by:

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A: The product rule of derivatives states that duv=u'v+v'u.

Q: Calculate the derivative of the following function. 7 y = sin '(cos (3x)) If the Chain Rule only…

A: To find the derivative

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Q: 1 Find the derivative of g(x)= (x)sec(x) + a+ x* + cos - sin(x)

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A: We will prove the given statement.

Q: 13. Find the derivative at x = a for f(x)= /sin(4x) 2 Vsin(4a) cos (4a) Jsin(4a) 2 sin(4a) Vsin(4a)…

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Q: Evaluate the derivative of y = sin'6x + In /1- 36x, where x= 0.125. dx |x= 0.125 U (Type an integer…

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Q: compute the derivative. y = sin(2x) cos2 x

A: We can find the derivative of this function by using the product rule of differentiation . According…

Q: Find the derivative of (a) (교2 + 1)" (6) In(cos²(e2")) 2x (c) sin-1 e-1 dt x +1 In a

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Q: 2. Use implicit differentiation to find the derivative of y with respect to x for the following: xe…

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Q: 12. The derivative of cos(1 – x) with respect to x is ;A. - sin(1 – x) B sin(1 – x) C -(1– x) sin(1–…

A: Given that: Let f(x)=cos(1-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: We have to find the derivative.

Q: The derivative of: y =0( sin (In (0))) in (In (0))) + cos(ln (0)) is is:

A: Given function is rewriting in other variables as: y=x(sin(ln(x)))+cos(ln(x)) Product rule of…

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

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Q: Find the derivative: 1+ e2x = cos 1 - e6x f(x) f'(x) =

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Q: Assuming that the derivative of arcsin(x) is indeed 1/√1 − x2, supply the justification that allows…

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Q: g(x) = cos ¹x+ 1-x

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Q: Find the derivative of y with respect to x, and 0 as appropriate: y = 6(sin (In 6) + cos (In 6) а.)

A: Given equation is: y=θsinlnθ+coslnθ Differentiate each term of y with respect to θ:…

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

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Q: ) .3 Find the derivative of h(x) = cos (2x – 5 %3D

A: Given,            hx=cos42x3-5To find : The derivative of the given function.

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Q: If y- sin x and yn) means "nth derivative of y with respect to x", what is the smallest posilive…

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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.

Q: k(x) = x In x %3D

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

A: we are given the function is  f(x)=1+sin2x2cos3x

Q: 5. Find the derivative of the following. 3x-5 а. у3 b. y = In (sin(3x-5)) c. y= e2x arc tan (2x + 3)…

A: Explanation of the answer is as follows

Q: Find the derivative of y=x?sinx x?cosx +2xsin x 2xcos x x2 sin x+2xcos x x2cosx

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Q: Find the first derivatives of y = cos x tanx

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Q: Use your knowledge on Higher-order derivative and Chain Rule to show that z" + 4z' + 8z = 0 if z =…

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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: 3. Find the derivative of (a) f(x) = (x + 2 sin x) (1 – 6 cos x), and (b) g(x) = sin x/ 7x

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Q: What is the derivative of the: y = (1 + cos2 x sin x2)3/2

A: Given: y=1+cos2x sinx232 differentiate with respect to x, dydx=ddx1+cos2x sinx232dydx=321+cos2x…

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A: Find the derivative of function

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A: we can answer only three subparts, or the first question and the rest can be reposted. No more than…

Q: The derivative of: y =0(sin (In (0)))+cos(In (0 )) is:

A: Given :y=θ(sin(ln θ))+ cos ln θ dydθ=θcos ln θθ+sin ln θ-sin  lnθ θ      =cos ln θ+sin ln θ-sin  lnθ…