Find the derivative of the following functions: [1 mark 1 12+5 (a). f(z): [0.25 Mark] T2 - 5 (b). f(z) = 2 tan'(x) – 67 [0.25 Mark] %3| | (c). f(z) = (z+ 5 sin z) (1 – 6 cos z) [0.25 Mark] %3D tanx (d). g(x) = [0.25 Mark] secr

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A: We differentiate with respect to t using chain rule.

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Q: Use three-point midpoint formula to evaluate the first derivative of y = cos(x) at x = 5 using a…

A: Given function is y=cosx. We have to find the first derivative of y=cosx at x=π2 using a value of…

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

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Q: 3. Find the derivative of the function. y = In(t2) – arctan(-

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Q: Find the derivative of the function y = arctan x + x 1+x²

A: Given: y=arctanx+x1+x2Recall the formulas:ddxarctanx=11+x2     ..........1ddxuv=vdudx-udvdxv2…

Q: Use forward-difference formula to evaluate the first derivative of y = tan(x) at x = 1 using a value…

A: The two-point forward difference formula to calculate f'(x) is f'(x)=f(x+h)-f(x)h, where h is the…

Q: find the derivative of y with respect to the appropriatevariable. y = (1 - θ) tanh-1 θ

A: Consider the following equation:

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Q: Find the derivative of y with respect to 0 y = 8e°(sin e - cos €) O 16e° sin e 8e (sin e - cos 0) +…

A: Given. We are given function of Y and theta and we need to find the function dY/d theta The concept…

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Q: Find the derivative of y with respect to the appropriate variable 65. y = sV1 – s² + cos¯s 66. y =…

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Q: Find the derivative of the function.

A: Given: y=lncosxcosx-1

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A: Given function is y=cos-1x2. Chain rule of differentiation states that: ddxfgx=f'gx·g'x…

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Q: find the derivative of y with respect to the appropriatevariable. y = ln (tan-1 x)

A: The given function is y=lntan-1x

Q: 1) Find the derivative of the function 2 + X y = arctan V 2 – x .Simplify where possible.

A: Answer and explanation is given below..

Q: Find the derivative of the function. y = 3 x tanh-1 x + 3 In/1 - x2 y' =

A: Product Rule of Differentiation : d(u.v)dx = u.dvdx+dudx.v

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A:

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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.

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Q: the derivative of y with respect to v. 1 = In ( cosh (5v)) –· tanh 2(5v) 2 derivative of y with…

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Q: 1+ cos x y = In 1-cos x

A: This question is based on chain rule differentiation.

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Q: (3e)® arctan (3x³) In(e2«) arccos(5x) 1. Find the derivative of f (x)

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Q: find the derivative of y with respect to the appropriatevariable. y = (θ2 + 2θ) tanh-1 (θ + 1)

A: The given function is y=θ2+2θ tanh-1θ+1. Obtain the derivative as follows.

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Q: a*+1 +1 t4 +1 dt with respect to x. Calculate the derivative ol Jsin(x)

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Q: find the derivative of y with respect to the appropriatevariable. y = sec-1 (2s + 1)

A: The given function is y=sec-12s+1.

Q: Use forward-difference formula to evaluate the first derivative of y = tan(x) at x = 4 using a value…

A: Given function is y=tanx. We have to find the first derivative of y=tanx at x=π4 using a value of…

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A: Given: y=4cos x+1tan x

Q: 1) Find the 3rd derivative of y = sin(x) %3D

A: To find the 3rd derivative of y=sinxx. Solution: For finding third derivative, we need to find first…

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Q: 1. y = cos2(2x − 1)

A: " Since you have asked multiple question, we will solve the first question for you. If you want any…

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

A: dydx=?

Q: find the derivative of y with respect to the appropriatevariable. y = sinh-1 (tan x)

A: The given function is: y = sinh-1 (tan x) The derivative of y=sinh-1θ is: ddθsinh-1θ=11+θ2.

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = (cos θ) ln (2θ + 2)

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Q: Find the derivative of the function. 11) y = cos x4 A) dy -4 sin x 4 B) dY - sin x4 dx C) dy - -4x4…

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