Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the expression in the lowest possible form. a. y = sinh(3x² ln(1 + 3Vx))

Q: y = In(x + Jx² +1)

A: This question is based on differentiation.

Q: Find the following derivatives: 1) y = sincos2x?

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Solve for the derivatives of the following functions with complete solutions. Use a separate sheet…

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Q: Find the derivatives of the functions y = x2 cot 5x

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Q: Find the second derivative (y") of the following function step-by-step and simplify the final…

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Q: Find the derivatives of the functions r = √(2θ sin θ)

A: Product rule of derivativef'u.v=v f'u+u.f'v or   u.v=u'v+v'uQuotient rule of…

Q: A. Solve for the Derivatives of the following functions. Final answers should be in simplified form…

A: Given y=tan-1(4sinx3+5cosx)

Q: Find the derivative of y with respect to 0. y sech P. sech 1. 5. (Type an exact answer, using…

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Q: Solve for the first, second, and third derivatives of y = 1/(4 + x) and then find a formula for its…

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Q: In the given question/s , find the derivative of the function.   y = ln l sin x l

A: Consider the function: y=lnsinx

Q: 1. Find and simplify the indicated derivative: (a) D: [e¯t sin(2t)]

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Q: -X sinh 1+x

A: This is the hyperbolic function.  We will find the derivative of the problem.  We know,  d/dx…

Q: a. y = f(x) = x' In(e?) %3D

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

Q: I Find the second derivative(y") of the following functions and simplify the final results. 1. y = x…

A: Some of the properties of derivative ddx(uv)=udvdx+vdudx ddxxn=nxn-1…

Q: y = sin(cos x)

A: Given:- y = sin(cosx)  To find:- Derivative of given function

Q: In the given problem, we implicitly differentiate by taking the derivative with respect to x of both…

A: Given  ddx(y)=ddx(5cos(x+y))

Q: 2+x 9 y = Arctan(- 1-2x

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Q: Find the derivatives of the functions r = 2θ√cos θ

A: Given: r=2 θ cosθ To determine: drdθ

Q: tan(xy) + xy = 0

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Q: Find the derivative d/dx of the following 1 log sin(x)

A: We can find the derivative as below

Q: y= Arccos(e2x)

A: Given: y=arccose2x To Find: The second derivative y'' of the given function and to simplify the…

Q: x² d. Find dx (e" -tant)dt. tan(x?) a. 2x(e** - tan(x?)) Ob. 2xex - sec?x O c. O d. It is impossible…

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Q: 28) y = tan² 2 29) y = In ln x 30) y = (x In æ)²

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Q: Find the derivatives of the functions y = 5 cot x2

A: Given: y=5cot x2Differentiation formula:ddxcotx=-cosec2xddxxn=n .xn-1

Q: y у %3D sin(3x + 2)

A: Use rules of differentiation

Q: e(2x- y) = 2x – y

A: Consider the function e2x-y=2x-y The given function is implicit function. Differentiate the function…

Q: . Find the derivative of the following functions and simplify the answer: ly = 4x² cos x- 10x sin x…

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Q: 2x y= Arccos(e)

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Q: Find the indicated derivatives: 1. of y = sin(3x + 4y) dx

A: The given function is: y=sin(3x+4y) The derivative of the sine function is: ddxsin(x)=cos(x) From…

Q: Find the derivative of y = cos³*+8 (x). Provide your answer below: y =

A: Given query is to find the series of the expression.

Q: Find the derivatives of the following functions: a) y2 sin x – tan (x + y) + 3x = 0

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Q: Find the derivative of the trigonometric function. y = cos((?x)8)

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Q: Find the indicated derivative. Then find an equation of the tangent line at the indicated point on…

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Q: (væ) + log, (5x² – 3) + ex² Find the derivative of y = arc tan

A: Explanation of the solution is given below...

Q: Find the derivatives of the functions y = θ3e-2θ cos 5θ

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Q: Find the derivatives of the following. 1. y= sin (e**+ 2x +5)

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Q: Q2/ Find the derivative 1. sin(xy)= of each of the following functions:- 2. y =(Inx)³ 3. y=cos (sin…

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Q: 3x Write down the derivative of the function V3+ cos? (x) dxc.

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Q: Solve the problems below: 1. Find the 25 derivative of y=x. 2. Find the nth order derivative of the…

A: 1. Consider the given function, y=x20 the first derivative of the function will be,…

Q: cos(xy) + secy = 5

A: Given: cosxy+secy=5 We know that  ddxcosx=-sinx…

Q: Find the derivatives of the given functions. a. y = [ Arc sec(tan x)|· e »<2x

A: use logarithmic function to evaluate the derivative.

Q: Solve the given item below and write the answer on a separate sheet of paper. Find the second…

A: Given  Cos(y) = x We need to find d²y/dx² We need to apply chain rule and product rule to solve…

Q: Find the derivative of the function. (®) = cos(6?) f'(0) =

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Q: - 7x Find the derivative of the function y =e sin 3x.

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Q: Solve for the derivatives of the following functions with complete solutions. a. y = In (5x²) b. y =…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: f(x) = e²x cos(x)

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Q: 2x Sin 1+x?

A: Evaluate the derivative of the given function as follows.…

Q: . Arcsin(x/y) = 4x + 3y

A: Solution :-

Q: 4. y = x0sx

A: Take the logarithm then take derivative twice.