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# How do you differentiate the function sin^{2}x.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 sin^{2}x.cos x, we get (2 sin x cos^{2}x - sin^{3}x).

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 sin^{2}x.

⇒ d (sin^{2}x)/dx = 2 sin x cos x (using the chain rule)

Now, applying the product rule in the given expression:

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

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

⇒ d (sin^{2}x.cos x)/dx = 2 sin x cos^{2}x - sin^{3}x

### Hence, when we differentiate sin^{2}x.cos x, we get (2 sin x cos^{2}x - sin^{3}x).

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