So Væ' (t)² + y' (t)² dt = 0.

Q: Compute the derivative of the function F (x) = L evi dt.

A:

Q: y = (r² + 4r) e"

A: given question is solved with the help of product rule of differentiation    i.e. (f.g)' = f*g'+…

Q: find dy/dx, when y=13(20-x4)5

A: To find , when .

Q: d mula sinh (t) = In (t + VE? + 1) and- (In(t)) = } %3D ne derivative of sinh(t).

A: Here we use rule of differenciation to find the required derivative.

Q: Find y' and y "   y =x2In(2x).

A: Given: y= x2ln2xDifferentiation Formula:ddxlnx=1xddxxn=nxn-1ddxuv=uv'+vu'

Q: Find dy/dx

A: Given expression,

Q: DX-X-5x+4, X(0)=X Dt

A:

Q: 8. Find the derivative of y = In(3t) dt.

A: To Determine: Find the derivative of given integral:…