dy 7. J У Vу2 -бу + 5 y V8 — х2 8. dx

Q: Differentiate. x4 y: 3 — х3 y' У -

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Q: If x²y + 3y* = xtan(y) + 2x d²y Find the value of dx²"

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Q: (2x+3) 8. S- (x2 +x+2)2

A: Let's find.

Q: 3 da IV9z2-4 o+ (z등) o 음sec-l (금) + C ○ 을sin-1 (을피) + C 0 3sin-1 (을2) +C O 3 sec -1. (을띠) + C

A: This question is based on indefinite integral.

Q: dx Vx? + 2x + 5

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Q: tnx Find if u=5 y=

A: The expression of dydxfor the following function needs to be evaluated : y = ln(x)x5

Q: Calculate 2 3x-2x²+2 dx. 13 -1

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Q: 32. Į 9** x? dx

A: To Determine: find the integration  Given: we have an integral ∫9x3x2dx Explanation: we have an…

Q: -| Vx³ + 16x² dx

A: Let I=∫x3+16x2 dx I=∫xx+16 dx Let assume x+16=t2⇒dx=2t dt I=∫(t2-16)t(2t) dt =2∫(t4-16t2)dt

Q: 3—4х dx =? Vx2+6x+1

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Q: 2-у (бх + 2у?)dx dy -2

A: On solving this we will get

Q: dy х3 + ху? dx 12 ||

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Q: Evaluate dx x3 – 2x2 + x

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Q: da d²y +6- dx dx² + 11 dx+6y = ex + cosx бу

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Q: dy d. dx = y(xy3 – 1)

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Q: Solve the diff eq (ху?+x-2у+3)dx +(x?у — 2х - 2у)dy %3D0

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Q: 2. dx 2. Solue integra

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Q: 1 dx 2 21+2*2 ху

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Q: Evaluate and simvlify y'. sec 2w y sec 2w + 1

A: Given: y=sec2wsec2w+1

Q: Solve ÿ + 6ỷ + 9y = 0 dy + 2y = e-4 dx d²y + y = 0 dx2 dx²

A: Note : There are multiple questions. Here is the solution of first question. Given differential…

Q: 4. Find y': y = 3x7 – 14x6 + 42 %3D

A: Given that:   y=3x7-14x6+42

Q: Calculate y" and y"'. y = x4 − 25x2 + 2x

A: Use the power rule and sum rule and difference rule of derivative:

Q: ди y ду ди dx

A: Solution

Q: Differentiate, hcx) = In (x-Vr

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Q: 3. Evaluate ry? dz dr dy.

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Q: 6. 19-x

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: udx + (1 - 3u)x du = 3u du.

A: I have stated the used formulas in the solution

Q: 3х +2 dx Зд2 + 4х + 1

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Q: (2+h)* Use the definition of the derivative to evaluate lim h+0 h

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