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: dy ) - /1 – x² find? dx y = x sec-1

A: Consider the following equation: y=xsec-11x-1-x2 Differentiate the above equation with respect to x:…

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: = Z

A:

Q: y = (1+) - (1+)*

A: We have to find dy/dx for the given function.

Q: D-the derivative is y = In In (VW) 1 +

A: The objective of the question is determine the derivative of the given function.

Q: Find dy/dx

A: Given expression,

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

A:

Q: If A = 4x³ and (a) TRUE (b) FALSE dt dx 2, then dA dt = 150.

A: As we know the Power law; ddxxn=nxn-1 Given: A=4x3 and dtdx=2

Q: solve du/dt = 1 + sqrt(u-t)

A:

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

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