Question

Differentiate Y = Sin(x² + 5)​

Answer 1

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⚘ Let f(x) = sin(x² + 5)

⚘ y = sin(x² + 5)

We need to derivative Y , w. r. t. x

$\huge{ \frac{dy}{dx} = \frac{d(sin( {x}^{2} + 5)) }{dx} }$

⇒ cos (x² + 5) × $\frac{d( {x}^{2} + 5) }{dx}$

$\boxed{sin \: x' = \cos \: x }$

⇒ cos (x² + 5) × $\frac{d( {x}^{2} )}{dx} + \frac{d(5)}{dx}$

⇒ cos (x² + 5) × ${2x}^{(2 - 1)}$ + 0

⇒ cos (x² + 5) × 2x

⇒2x cos (x² + 5)

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Answer 2

Answer:

2xcos(x^2 + 5)

Explanation:

y = sin(x^2 + 5)

diffrenciating with respect to x we getc

dy/dx = d(sin(x^2+5)/dx *d(x^2+5)/dx

dy/dx = 2xcos (x^2 + 5)