1- Evaluate: 2y sinx dy dx อน 2- If u = x² + ey², x = sin 2t , y = cost² find Ət

Q: What is dy/dx for y=cos(sinx)? O a) dy/dx = -sin(cosx) Ob) dy/dx = sin(sinx) O c) dy/dx =…

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Q: (f) / sec“ y dy. tan5

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Q: Differentiate y = (-6+sinx)/(x+cosx)

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Q: ) Find y' sin)= 8x+y

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Q: S tan — х) dx

A: To integrate: ∫tan(x4-x)dx Solution: Given, ∫tan(x4-x)dx On simplifying further we get:…

Q: d 1+ sin² (2)| dz

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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: (tan V) (sec V) b) Evaluate dx

A: Given integral: I=∫tan4(x)sec2(x)xdx

Q: QS A) Find IF y = - Ve IF y =-Vt and t sinx

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Q: 8. f sec² (3x - 1) dx

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Q: Solve cosx dx + (sinx)y=1 Select one: O ay sinx + ccosx O b. y = 2sinx + 2cosx + c O c. y = sinx –…

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

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Q: A particular solution of y" + y =sinx + xcosx a. x?sinx - 2xcosx) 4 b. (x?sinx – xcosx) 4 c. (x?sinx…

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Q: Differentiate  (sin 2t)/t.

A: ft=sin2tt

Q: 3D5 in.

A: The area of the circle can be computed using the formula: Area=π r2 Where, 'π' is the constant value…

Q: Find / 5x dx

A: ∫Axndx =A(xn+1n+1)+C, where C is integration constant.

Q: Y"+y=secxtanx

A: Given, y'' + y = secx tanx This is a second order linear, non-homogeneous ODE. We can write the…

Q: sinty

A: This is a basic integration problem

Q: dy - (1+x)у -ху? .2 1.) х- dx

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Q: H.w Sec'c-x)=バーSec x

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

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Q: Find Sor y. Sin X- xp X+1

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Q: Calculate as ;(x sin y + e).

A: First partially differentiate with respect to 'y' three times and then partially differentiate with…

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

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Q: 2. v = e-sinx

A: Given