Question

differentiate cos (1-x^2)^2​

Answer 1

We have to differentiate :-

$\cos( {1 - {x}^{2})}^{2}$

We will differentiate the above expression by using chain rule :-

$\implies \: \dfrac{d(\cos( {1 - {x}^{2})}^{2} )}{dx}$

$\implies \: - sin{(1 - {x}^{2})}^{2} \times \dfrac{d(( {1 - {x}^{2})}^{2} )}{dx} \times \dfrac{d( {1 - {x}^{2})} }{dx}$

$\implies \: - sin{(1 - {x}^{2})}^{2} \times 2(1 - {x}^{2} ) \times ( - 2 {x})$

$\implies \: 4 sin{(1 - {x}^{2})}^{2} \times (1 - {x}^{2} ) \times x$

$\implies \: 4 x (1 - {x}^{2} ) \: \: sin{(1 - {x}^{2})}^{2}$

$\implies \: 4 (x - {x}^{3} ) \: \: sin{(1 - {x}^{2})}^{2}$

Answer :

$4 (x - {x}^{3} ) \: \: sin{(1 - {x}^{2})}^{2}$

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$\large\bf\blue{Additional-Information}$

d(sinx)/dx = cosx

d(cos x)/dx = -sin x

d(tan x)/dx = sec²x

d(cot x)/dx = - cosec² x

d(cosec x)/dx = -cot x cosec x

d(sec x)/dx = secx tanx

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