Differentiate the function with respect to x.  2√cot(x²)

Solution:

A derivative helps us to know the changing relationship between two variables. Consider the independent variable 'x' and the dependent variable 'y'. 

Let f(x) = 2√cot(x²)

⇒ d/dx [2√cot (x²)]

By using chain rule of derivative, we get

= 2.1/2 √cot (x²) × d/dx [cot (x²)]

= √sin (x²) / cos (x²) × − cosec² (x²) × d/dx (x²)

= √sin (x²) cos (x²) × − sin²(x²) × (2x)

= −2x / sinx² √cos x² sin x²

= −2√2 x / sin x² √2 sin x² cos x²

⇒ d/dx [2√cot (x²)] = −2√2 x / sin x² √sin 2x²

NCERT Solutions Class 12 Maths - Chapter 5 Exercise 5.2 Question 7

Differentiate the function with respect to x.  2√cot(x²)

Summary:

The derivative of the function with respect to x of  2√cot (x²) is  −2√2 x / sin x² √sin 2x²