# Differentiate the function with respect to x. cos x^{3}.sin^{2 }(x^{5})

**Solution:**

Let f(x) = cos x^{3}.sin^{2}(x^{5})

⇒ d/dx [cos x^{3}.sin^{2}(x^{5})]

If a function is lying inside the given function then we say the function is composite.

Since the given function in the problem is a composite function.

It can be solved by using the chain rule of derivatives.

i.e we need to differentiate all the functions present in the problem separately and then multiply at the end.

By using chain rule of derivative.

we get

= sin^{2}(x^{5}) × d/dx (cos x^{3}) + cos x^{3 }× d/dx [sin^{2}(x^{5})]

= sin^{2}(x^{5}) × (− sin x^{3}) × d/dx (x^{3}) + cos x^{3 }× 2sin (x^{5}).d/dx [sin x^{5}]

= −sin x^{3}sin^{2 }(x^{5}) × 3x^{2 }+ 2sin x^{5}cos x^{3}.cos x^{5 }× d/dx (x^{5})

= −3x^{2}sin x^{3}.sin^{2 }(x^{5}) + 2sin x^{5}cos x^{5}cos x^{3 }× 5x^{4}

⇒ d/dx [cos x^{3}.sin^{2}(x^{5})] = 10x^{4 }sin x^{5 }cos x^{5}cos x^{3 }− 3x^{2 }sin x^{3}sin^{2 }(x^{5})

NCERT Solutions Class 12 Maths - Chapter 5 Exercise 5.2 Question 6

## Differentiate the function with respect to x. cos x^{3}.sin^{2}(x^{5})

**Summary:**

By using chain rule of derivative, we get the derivative of the function with respect to x. cos x^{3}.sin^{2}(x^{5}) is d/dx [cos x^{3}.sin^{2}(x^{5})] = 10x^{4 }sin x^{5 }cos x^{5}cos x^{3 }− 3x^{2 }sin x^{3}sin^{2 }(x^{5})