2x [In sin to where in #2, V=In sing y-x (1-x²)]|dx + (1-x²) cot y dy dv=; du shy cosy dy = coty dy sin

Q: Differentiate (a). y = 23z+sin z² %3D (b). y = r³3=

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Q: X sec10 can 1. Let u = 7 In х2 - 1

A: Given: ∫x sec107ln2x2 - 13tan7ln2x2 - 13dxx2 - 1.

Q: e-i.dt = lim X+ 00 V TE 0, Select one: a. b. NOT C. 8, O d. 1 O e. 0

A: According to our guidelines we can answer only first question. In first question we use the concept…

Q: d'y For y= 2cos +5sin x, if =m sinx+n cosx, dx2 then 2m+n=

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Q: hpxp(₂h + x)us hx [V² [V² Find

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Q: sin x Find dy/dx given that y 1+ cos x

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Q: x sec? x? dx; u = x' see2

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Q: Differentiate f(r)= (3x² + 10 – sin r)º. -

A: Given:- f(x) =(3x2+10-sin(x))  To find:- Derivative of f(x)

Q: 2- Find dy/dx for y = In(tan(2x²))

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Q: find ody dx 4= Sin 3X

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Q: cos' v dv 1-sin v 2.

A: Given

Q: If y=sin(tan(3x)), then dy dx Check = Select one: O a. 3cos (tan(3x))sec²(3x) O b. cos…

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Q: dy (2x sin h -+3y cos h -) dx Зх cos h - 2 tan h 3 + ||

A: According to the trigonometric hyperbolic formula: tanh(x)=sinh(x)cosh(x)        ...(i) Distributive…

Q: Let dy Then = dx y = tan -¹(√42²-1)

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Q: | sin x (3cos*)dx 2:

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Q: Let dy Then dx -1 y = tan ¹ (√4x²

A: Let To find .

Q: [x³J2]=x³J2 dx ulgn O ihs O

A: Solution: Since J2=∑s=0∞-1s2+s!s!x22+2s Then, x3J2=∑s=0∞-1s2+s!s!·x3x22+2s…

Q: x' cos“ x sin x dx. (л- Злх + 3х Evaluate: | -

A: For the solution of the problem follow the next steps.

Q: Evaluate:

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