Example 1: z=x³y_x=2t and y=t² Find dz dt

Q: Find dy/dt.

A: Given, y=9-4x3+2x; dxdt=-1,x=-3 To find dydt

Q: Find at æ = 3 if y=-5x² - 2 and da dt dy dt = 4.

A:

Q: et y = f(x) = 5x² + 3x + 5 and x = g(t) = 2t + 3. Find dy = dy dt

A: Given query is to find the derivative.

Q: Find g'(x) if g(x) = t² cos 6t dt %3D 2

A: We can apply fundamental theorem of calculus here.  The second fundamental theorem of calculus…

Q: e"dt=

A:

Q: secx 1 Given g(x) : z dt , find g'(x). t2

A: gx = ∫7sexcx1t2dt           = ∫7sexcx t-2 dt        = t-2+1-2+7secx      =t-17secx-1 = secx-1-7-1-1…

Q: Find dx dt da dt at x = 5 if y=-x² - 1 and dy dt 1.

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Q: Let x+y = 100,if dx dy = 2, find dt when y-6 and x-8 %3D

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Q: dy at x = 1 if y = 4x² + 1 and dt dx Find – 1. dt dy dt || ||

A: Solve the following derivative

Q: y? what is dt/dy? 2y +1 if t =

A:

Q: Find dy/dx

A: We have to find  dydx where y=∫0xt3+110dt3

Q: 8. Find dw/dt if w= xr^yz, x=t^3, y=1+t, z=1+2t

A:

Q: sinh x d Find dx 1 dt t2 + 1

A: We will apply Leibnitz theorem to solve it

Q: dy Find at x = dt – 4 if y = dx - 2x2 + 3 and dt 2. - - dy dt ||

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Q: dy dt : 2y + y5 =

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Q: 1 So 2t en + e-2t ezt - e-at dt

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Q: solve using ODE from t=0 to 2 when y(0)=1 dy/dt= yt^3 - 1.5y

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Q: t2-6t+9 dy 3. y = 2-5t+6' dt (t+1)(t²–1) dw 4. w = t2+2t+1 dt

A: follow next step

Q: find dy/dt Y= (1+cos4t)^5

A: