Question

Find d^2y/dtheta^2 if y=sin^5

Answer 1

20 sin³O. cos²O - 5sin⁵O

Explanation:

y = sin⁵O

Using the Chain Rule

dy/dO = 5 sin⁴O cosO

Using the Product / Chain rules:

d²y/dO² = 20 sin³O.cosO . cos O+ 5 sin⁴O * - sin O

= 20 sin³O. cos²O - 5sin⁵O