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# Differentiate the function with respect to x. 2√cot(x^{2})

**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(x^{2})

⇒ d/dx [2√cot (x^{2})]

By using chain rule of derivative, we get

= 2.1/2 √cot (x^{2}) × d/dx [cot (x^{2})]

= √sin (x^{2}) / cos (x^{2}) × − cosec^{2 }(x^{2}) × d/dx (x^{2})

= √sin (x^{2}) cos (x^{2}) × − sin^{2}(x^{2}) × (2x)

= −2x / sinx^{2 }√cos x^{2 }sin x^{2}

= −2√2 x / sin x^{2 }√2 sin x^{2 }cos x^{2}

⇒ d/dx [2√cot (x^{2})] = −2√2 x / sin x^{2 }√sin 2x^{2}

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

## Differentiate the function with respect to x. 2√cot(x^{2})

**Summary:**

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

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