Question

Find the derivatives of the following functions. log (cot(1-x²))​

Answer 1

Answer with Explanation :

let the function is ,

y = log (cot (1-x²))

Differentiation wrt x,

$\frac{dy}{dx} = \frac{d}{dx} (log(cot(1 - {x}^{2} )))$

$\implies \sf \frac{1}{cot(1 - {x}^{2} )} \times ( - {cosec}^{2} x(1 - {x}^{2} )) \times ( \frac{d}{dx} (1 - {x}^{2} ))$

$\implies \sf \frac{1}{cot(1 - {x}^{2} )} \times ( - {cosec}^{2} (1 - {x}^{2} )) \times ( 0 - 2x)$

$</p><p>\implies \sf \frac{ - 2x( {cosec}^{2} (1 - {x}^{2})) }{cot(1 - {x}^{2} )}$

$\implies\boxed{\sf -2x({\frac{({cosec}^{2}(1- {x}^{2}))}{cot(1 - {x}^{2} )}})}$

formulae used :

• d/dx(cotx) = -cosec²x
• d/dx(x^n) = n(x )^(n-1)
• d/dx(k) = 0