Question

Differentiate with respect to x 2√cot(X²)

Answer 1

$\implies \bf \dfrac{ d(2\sqrt{cot \: {x}^{2}} \: ) }{dx}$

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

We know that :-

$\underline{ \boxed{\bf \dfrac{ d({cot \: {t}} \: ) }{dt} = - \: {csc}^{2} t}}$

$\implies \sf 2 \times \dfrac{1}{2{(cot \: {x}^{2})}^{ \frac{ 1}{2} } } \times \: - {csc}^{2} {x}^{2} \: \times 2x$

$\implies \sf - \dfrac{2x \: {csc}^{2} {x}^{2}}{{(cot \: {x}^{2})}^{ \frac{ 1}{2} } }$

$\implies \sf \dfrac{ -2 x \: {csc}^{2}{x}^{2} }{ \sqrt{cot \: {x}^{2}} }$

Answer :

$\bf\dfrac{ d(\sqrt{cot \: {x}^{2}} \: ) }{dx} = \dfrac{ - 2x \: {csc}^{2} {x}^{2}}{ \sqrt{cot \: {x}^{2}} }$

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

d(sinx)/dx = cosx

d(cos x)/dx = -sin x

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

d(tan x)/dx = sec²x

d(sec x)/dx = secx tanx

d(cot x)/dx = - cosec² x

d(x^n)/dx = n x^(n-1)

d(log x)/dx = 1/x

d(e^x)/dx = e^x

Answer 2

Hey There

Here's The Answer

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• Reffer to the Attachment.

Hope it Helps.