How do you differentiate the function sin²x.cos x?

Differentiation or derivatives are one of the most important concepts in calculus. It is the reverse of integration. The slopes of various curves at different points can be found out using differentiation.

Answer: When we differentiate sin²x.cos x, we get (2 sin x cos²x - sin³x).

Let's understand step by step.

Explanation:

We must use the product rule as well as the chain rule to solve the problem.

Now, first, we calculate the derivative of sin²x.

⇒ d (sin²x)/dx = 2 sin x cos x   (using the chain rule)

Now, applying the product rule in the given expression:

⇒ d (sin²x.cos x)/dx  = { d(sin²x)/dx  × cos x } + { d(cos x)/dx  × sin²x }

⇒ d (sin²x.cos x)/dx = { 2 sin x cos x × cos x } + { (-sin x) × sin²x }

⇒ d (sin²x.cos x)/dx = 2 sin x cos²x - sin³x 

Hence, when we differentiate sin²x.cos x, we get (2 sin x cos²x - sin³x).