Solve for the second derivative(y") of the following and simplify the final results. Show complete solution. 4ln (Arctan x) = 1 – y

Q: The y' of the given function is (1–2 sin? 4x) y

A:

Q: Find the first derivative for y = 5 cos x

A: Given,          y=5cosx

Q: (væ) + log, (5x² – 3) + ex² Find the derivative of y = arc tan

A: Explanation of the solution is given below...

Q: Find the first and second derivative: y=x1/2+(4/x1/2)

A: First derivative:

Q: Solve for derivative. y = (x + cos x) ( 1 - sin x)

A: Given          y = (x + cos x) ( 1 - sin x)

Q: derivative of y = e(sin⁡x) − sin⁡(ex)8

A:

Q: Solve the first and second derivative of y = cosh2x+ sinhx

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: