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

Q: i. y= ) In (x+3

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Q: Find the differential of the function: y = x In x

A: Solution:Giveny=x ln xTo find the diffferentiationformula:(uv)'=uv'+vu'ddxxn=nxn-1ddxln x=1x

Q: In xy = x² + sin xy

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Q: find the derivative of y with respect to the appropriatevariable. y = ln (x2 + 4) - x tan-1 ( x/2)

A: We use the chain rule and product rule

Q: Is it possible to evaluate the anti-derivative below? | (x + 1) cOS (2x) cos (x2) dx

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

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Q: 1. Find the first derivative of the given function given. a. y = sint cos t b. y = 6 tan(2n + 3x)

A: In this question we have to find the first derivate of the given function.

Q: find the derivative of y with respect to x, t, orθ, as appropriate. y = esin t(ln t2 + 1)

A: The variable is t in this equation  So we will differentiate with respect to t   We will use the…

Q: Find the differential of the function y = x- sin x.

A: Given: y=x2-sinx

Q: The derivative of the function y = sin-1(e* – In x), where Je – In x| < 1, is:

A: Recall ddx(sin-1(x))=11-x2 ddx(ex)=ex ddx(ln(x))=1x

Q: Find the derivative of the function.

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Q: Find the derivative of y with respect to x. y = 2x 4 sin -1 x

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Q: Find the derivative of y with respect to x. 2. y²(x + 2y) = e²

A: Given,

Q: Can you help me step by step?

A: Differentiate with respect to x,

Q: Find the derivative of the inverse trig functions. a) y = cos-1 5x b) y = x· arctan x

A: We can solve both the question as below.

Q: find the derivative of y with respect to x, t, or u,as appropriate.13. y = ln (t/2) 14. y = ln…

A: Given question is to find the derivative of the function , which can be solved by using the chain…

Q: Find the derivative of the function. sin(x) y = In(1 + 6v) dv cos(x)

A: Find the derivative of the following function

Q: find the derivative of y with respect to the appropriatevariable. y = cos-1 (x2)

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

Q: Find the derivatives of the functions y = ln cos-1 x

A: The given function is y=lncos-1x.

Q: b)Find the derivative of the function x cos (2x + 3y) = y sin x

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Q: The derivative of the function 3+ln x is: y = cos(In x)

A: y=3+ln(x)cos(ln(x)Differentiate w.r.t.xApply the Quotient Rule:  fg'=f…

Q: Find the derivative of the function. 1- e3x 1 + e3x y = cos y' =

A: Given that: y = cos1-e3x1+e3x To find: We have to find the derivative of the given function.

Q: Find the derivative of y=ln(cos(z))

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Q: Can you help me step by step?

A: We need to find the derivative of the given equation.

Q: Find the derivative of the given function. y = x² sin 'x+x cos 4x

A: For     y=fx gx    dydx=fx ddxgx+gxddxfx   This is the multiplication rule of derivative .

Q: find the derivative of y with respect to x, t, or u,as appropriate.55. y = ln (cos^2 u) 56. y = ln…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

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, t, or θ, as appropriate.

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Q: Find the derivative of y=2ecos.x)(sin(5x)) d'y Calculate as a function of t if x=t-t and y=t-t 2 dx?…

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Q: Find the derivative of y with respect to x. y = 6x° sin -1 (6x) + /1- 36x° dy dx II

A: Given function is By using product rule of differentiation, we get

Q: y = cof'/ x2-1 x²+

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Q: A-The derivative is y = In sin 0 cos 0 1+2 ln 0

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Q: Find the derivative of y = x 1 cOS x 2

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Q: Find the derivative of y with respect to x. Y=ln(13/x) dy/dx

A: Given, y=ln13x we have to find derivative of y with respect to x.

Q: derivative of a Y with respect to x Y= ln (15x)+3x dy/dx=

A: Use formula of derivative to solve

Q: Find the derivative of the given function. 2 y = x sin x+x cos -3 dx

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Q: Find the derivative. d | dx + 0 OA. x³ sin (x¹) +5, ○ B. sint dt C. 4x³ sin (x4) - cos (x4) - 1 D.…

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Q: Find the derivative of y with respect to x.

A: Given:The function

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

A: On simplification, we get

Q: Can you help me with this problem step by step?

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Q: Find the derivative of y with respect to X Y=cos^-1 ( 3x^7) dy/dx=

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Q: Find the derivative of y with respect to x for y = (- 7x2 – 5x + 5) (sin x + 11x) 1x + ..... The…

A: Given:- y = (-7x2-5x+5) (sin(x) +11x)  To find:- Derivative of y

Q: Find the derivative of y with respect to the given independent variable. e* cos' x (1) y= x+1

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Q: Find the derivative of y= cos with respect to x. -1 The derivative of y= cos with respect to x is 1

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Q: can you help me step by step with this problem?

A: Let z= 6x^2+1 Substitute that. Then take d/dx on both sides.

Q: Find the derivative of y with respect to x: ,2 2 X'e y = log,2 x+2) Evaluate the integral: -1 cos…

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Q: V=ln( cosn 92) %3D

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Q: Find the derivative of y with respect to x. Y=(x^2 ln x)^4

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: