Question

Differentiate the following:
cos²x³

Answer 1

$\implies {cos}^{2} {x}^{3}$

We have to differentiate the above expression.

$\implies \dfrac{d( {cos}^{2} {x}^{3} ) }{dx}$

Differentiating using Chain rule:-

$\implies 2cos \: x \times \dfrac{d( {cos} \: x) }{dx} \times \dfrac{d ({x}^{3} )}{dx} \times \dfrac{dx}{dx}$

$\implies 2cos \: x \times ( - {sin} \: x) \times3 {x}^{2} \times 1$

$\implies - 2cos \: x \times{sin} \: x \times 3 {x}^{2}$

We know that :-

$2cos \:{sin}x \: = \sin(2x)$

$\implies - (2cos \: x \times{sin} \: x) \times 3 {x}^{2}$

$\implies - (2cos \: x \: {sin} \: x) \times 3 {x}^{2}$

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

$\implies - 3 {x}^{2} {sin} \: 2x$

Answer :

$\implies \dfrac{d( {cos}^{2} {x}^{3} ) }{dx} = - 3 {x}^{2} {sin} \: 2x$

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Learn more :-

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

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Answer 2

Step-by-step explanation:

cos becomes -sin after differentiation