In SRSWOR show that E(y )= Y

Q: y(x) = tan{/3x² + In(5x*) - In(5x'

A: Given  y(x) = tan3x23 + ln5x4 We have to find dydx.

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

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Q: xe 2, x Cosz dx

A: Integration by parts, ∫udv=uv-∫vdu u is the first function Given integral, ∫x exdx

Q: Integrate (x)(e^-x)dx within the limits of (1, infinity)

A: Givne that  Integrate (x)(e^-x)dx   limits of (1, infinity)

Q: In(x) 1. Evaluate -dx if possible. If not possible, explain why.

A: As we know that the integration by parts:- ∫udv=uv-∫vdu

Q: Latel I, Vx2 + y² dV,

A: answer is in next step

Q: If X and Y have joint pdf given by

A: From the given information, fX,Yx,y=2I0,yxI0,1y                =2, 0<x<y, 0<y<1

Q: OFind the second derivative of y = 4Vx + E + 10

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Q: 28. Differentiate implicitly to find dy/dx if x + x/y = 7.

A: Given, x3+x/y=7 we can also write as yx3+x=7y,  or y=x7-x3 derivate both side w.r.t x…

Q: 9. Vy + dy 415

A: We will be using the given rules to evaluate the answer

Q: Sinh) esechct) dy

A:

Q: 15 dy dt 2-

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Q: dy log x If xY = ex-Y, prove that %3D dx (1+ logx)?

A: Introduction :

Q: Find the indicated derivative. dp for p q² + 2 5q – 3 %3D dq dp dq II

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Q: At time t = 0, then th

A: P(t)=0.5t4-16t3+144t2       , 0≤t≤12At t=0 the sale begins,costco is having a 12 hour sale,The rate…

Q: Show that In(x") = y In(x) for all x, y > 0, only using the rules of derivative for the natural…

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Q: If X is an exponential RV with parameter A, find the PDF of Y = -14 In(X). 2

A: Given information: If X is an Exponential random variable with parameter λ. The pdf of X is,…

Q: Use a linear approximation (or differentials) to estimate the given number. (1.999)3

A: First I have find the linearization of x^3 near x=2 and then find the required approximated value.…

Q: In 5 x+1 Find the derivative of y = logs ((*)) with respect to x-1 independent variable x.

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Q: Differentiate. y =x° In x- dy II

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Q: Use a linear approximation (or differentials) to estimate the given number. (1.999)5

A: Given term is (1.999)5Let x = 1.999

Q: IPydx dy 20.

A: To evaluate: ∫02∫13 x3y dxdy

Q: d - In(u²) dt dx et

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Q: 4. Evaluate e*dx using integration by parts.

A: Explanation and solutions is given below.....

Q: What is the derivative of y = e3 In(5 + e3)? %3D

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Q: Find dy/dxin terms of x and y if ax^4−by^4=c^4 Assume that a, b and c are constants. dydx=…

A: Given : ax4-by4 = c4 a, b and c are constants. To determine dydx

Q: In (1 + 2), What is the derivative of y .? e2z %3D

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Q: Differentiate implicitly to find dz if xz + In(xy) + = 10.

A: Given an equation We have to apply the implicit differention to the equation

Q: use Gamma Function to evalute the Rollowinq e dy

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Q: Let e 2* = 2 find dy dx at x = 1

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Q: la y is not measurable. Wan

A: Given a statement

Q: Find dy ify Yify = sın 2x. dx

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Q: In 5 Find the derivative of y = logs ()) with respect to independent variablex.

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Q: Use a linear approximation (or differentials) to estimate the given number. e0.01

A: We use linear approximation to find e0.01 By linear approximation f(x)=f(a)+f'(a)(x-a) we take a=0…

Q: 4. Show that the derivative of log,(Va +5) is 3(r + 5) In(2)

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Q: 16 Evaluate ſ," x²In 3x dx correct to three decimal places.

A: Given- ∫12x2ln3x To find- The value of the above integral. Concept Used- The above integral can be…

Q: Sulve the dffeanlial equalion ly). clox Ylx)=16

A: Given:     dydx+y=16

Q: Find oy for dx2

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Q: y' – ey : = sin x

A: In this question, we have given a differential equation y'-ey=sin(x) here, we need to check either…

Q: Compute dy/dx for y = log3 x

A: Our Aim is to calculate dydx for the function given below:-y=log3(x) -(i)

Q: Find dy/dx implicitly. exy + x2 - y? = 11 |

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Q: show that the lim dose not exist x.y-00

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Q: Evaluate S 0 2-9.x² dx using the Gamma function.

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Q: 2. If f(x, y) = 1/(xy), the marginal pdf of X is (log x)/y.

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Q: (In x) dx Integrate: 1

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Q: The equation of the tangent line for the graph of Fx)= | Ln(P+4)dt at x=2 is F(x)=

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Q: 5. Implicitly differentiate the equation (xy)-y=x to find dx

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Q: If f(x, y) = 1/(xy), the marginal pdf of X is (log x)/y. TRUE or FALSE ?

A: