3. Find syz for ys = In(x + yz) – xcoth-1 log ().

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)2 + dx y * logy x *

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Q: dy 24// A- If y= cosh(t³ – 1)+ log2(3t + 1)10 - In (sin-1(e-t)), find dt B- Find a value of n so…

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

Q: Another equation that has been used to model population growth is the Gompertz15 equation dydt=ry…

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Q: Find d if z = log2 y - 6 logs y. In In 64 dz dz dy y In 2 In 5 dy y In 2 In 5 O Option 3 O Option 2…

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Q: 1) Find dy/dt for if : y = log2 (81ln 2) 2) Evaluate the following integral: In 2 " log2 (x + 2)* dx…

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Q: 1) Find dy/dt for if : y = log2 (81n 2) 2) Evaluate the following integral= In 2 log2 (x + 2) dx x +…

A: Any logarithmic function having a base other than e can b converted to a natural log as shown below:…

Q: 뿐 for the following: y = ln(e2z) 0 읊 ○ 2 Oezz ○ ez (In 2)

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Q: Prove that sinh−1 t = ln(t + √t2 + 1 ).

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Q: Answer the following using Homogenous ODE in Differential Equation. 3xydx + (x² + y²)dy = 0

A: Hint: By putting y=vx we can solve homogeneous differential equation.

Q: b) Suppose x # 2. Find dif dx In y = In (x - 2)² √x² +1

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Q: Suppose x4 e−4y = ln (xy).Find dy/dx by implicit differentiation.

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Q: Find the slope of the tangent line to the graph of x²-Iny=0 at x=2 O None of these O 4e4 O e4 O 4

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Q: Differentiate the following using chain rule Y = In (cot 3x – 2) Y = log cos? 3x

A: We need to find the derivative of Y=ln cot 3x-2 and Y=log cos23x. First problem: Now,…

Q: 1 Find the most general antiderivative of the function x3 + 4x

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Q: In(r) Find dy/dx using the method of logarithmic differentiation when y = (4+ 2x²).

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y logy x * * -

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Q: Find values of p for which integral diverges. dx x(In x)"

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Q: A 1125 m³ open-top rectangular tank with a square base x m on a side and y m deep is to be built…

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Q: If e (3x + 2)e2* dy 3 4 using logarithmic differentiation. (b) show that +2 2.x-1 %3D (2x-1) dx 3x…

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Q: 4. y = log,(x* +3x² +1)

A: y = log(x4 +3x2 +1 ) here we use chain rule for differentiation dy/dx = (4x3 +6x )/(x4 +3x2 +1 )

Q: Q1- Find dy / dx for the following functions: -2 2.8ln2 eo Y= 4 5 sinh 9x * Inxy sino 3 log2 2

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Q: Q1: Find dy/dx of the following functions: 1. x?e? y = log2 2Vx+1,

A: Disclaimer: Since you have posted multiple questions, we will be answering only first question for…

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y * logy x |

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Q: dy for y =loge(l-Sin( 3x) Xア

A: We use chain rule to solve this differentiation

Q: az dz +y =5 ax If z= log ( x+x*y+y° ), Prove that x

A: We can prove this using the rules of partial derivative

Q: Find the general form of the antiderivative of g(x) = - cos4x

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Q: From part U), | Be dx (4,1,2) = -7 JT sin (4x) | (4-1) In(3) ( log (33)² 3 ln (3) 3dn(3) A(4) gin…

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Q: 19.) [(ycoth y² )log°(sinh y² )dy

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Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = er+1) 3- xy +x*y = 3 at x = 1

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: Find the derivative, dy/dx: y = log3 (2x +1) Oy =- (2z+1)3 In 3 Oy = (2r+1) In 3- Oy= log, e (2z+1)3…

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Q: In (6x) to x if y = sin (5e') dt.

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Q: 04: Find dy/dx for the following function:: (5) y = x³ log₂ (3 - 2x)

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Q: Given that y = (In(x))²In(), find dy using the method of logarithmic d.x differentiation. dy %3D

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Q: Eliminate the arbitrary constants x = -ln t , y = at + bt^2

A: given  x=-ln t , y=at+bt2 claim- to eliminate the arbitrary constants

Q: 18. Show that Vxª + x and Vx* x→o by showing that they both grow at the same rate as x² as x' grow…

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Q: Determine for the following function: dy dx y = log3 (x² + 1) ○ (z²+1) In 3 2x O (1²+1) 2x O 2x…

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Q: dz +y ay dz 100 z= log ( x 100 + x50 y50 + y100 ), Prove that x

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Q: se N.P.M. to estimate the root of -X = e -X for an initial of Xo =0

A: Here f(x)=e-x-x,  x0=0. We estimate the root of f(x)=0 by using N.R.M.

Q: 3 7 use log differentiation to differentiate to find y prime (dy).   y = sin(x)x

A: Given function y = Sin(x)x , here we need to determine y\'.Let us use logarithmic differentiation.…

Q: a) the linear approxinma ion to the function + 3X ät

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Q: Find the net change in ve]locity over [1, 4] of an object with a(t) = 8t − t2 m/s2.

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Q: Find a differential operator that annihilates the given function. xe3xsin5x

A: given function is                                                      f(x)=xe3xsin5x we have to…

Q: (2) Find the derivative of the following: In xy = e*+y 4. %3D y = esint (In t² + 1) 5. y = In e 1+e…

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Q: 1) Find dy/dt for if : y = log2 (81ln 2) %3D

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Q: 4. y= log1,(x* +3x² +1) %3|

A: Given: y=log10x4+3x2+1   As we know that; The Power law; ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x…

Q: 1) Find dy/dt for if : y = log2 (81ln 2) 2) Evaluate the following integral In 2 * log2 (x + 2) dx x…

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Q: 4. Express the integral e-t tổ dt in terms of gamma function.

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Q: Find 뿐 for the ry – ln(xy) = 1 0 뽈 ㅇ-볼 O 래 ㅇ-픕 following:

A: The given expression is xy-lnxy=1 we have to find dydx use the derivative formulas, ddxx=1…

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)? dx y logy x

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Q: Find the general solution using Reduction of Order: x2y''-xy'+y=0 y1=ln x

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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: