Question

differentiate y = sin(x^2+5) with respect to x​

Answer 1

y = sin(x^2+5)

dy/dx = cos (x^2+5) .2x

dy/dx = 2x .Cos (x^2+5)

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Answer 2

ANSWER:

To Do:

• Differentiate sin(x^2 + 5) with respect to x

Solution:

$\text{We are given that,}\\\\:\longrightarrow y=\sin(x^2+5)\\\\:\implies\dfrac{dy}{dx}=\dfrac{d}{dx}\sin(x^2+5)\\\\\text{We know that,}\\\\:\hookrightarrow\dfrac{d}{dx}\sin\theta=\cos\theta\\\\:\hookrightarrow\dfrac{d}{dx}x^n=nx^{n-1}\\\\:\hookrightarrow\dfrac{d}{dx}constant=0\\\\\text{So, on applying chain rule,}\\\\:\implies\dfrac{dy}{dx}=\dfrac{d}{dx}\sin(x^2+5)\\\\:\implies\dfrac{dy}{dx}=\cos(x^2+5)\times\dfrac{d}{dx}(x^2+5)\\\\:\implies\dfrac{dy}{dx}=\cos(x^2+5)\times(2x^{2-1}+0)\\\\:\implies\dfrac{dy}{dx}=\cos(x^2+5)\times(2x+0)\\\\:\implies\dfrac{dy}{dx}=\cos(x^2+5)\times2x\\\\\bf{:\implies\dfrac{dy}{dx}=2x\cos(x^2+5)}$

Formulae Used:

$:\hookrightarrow1)\:\dfrac{d}{dx}\sin\theta=\cos\theta\\\\:\hookrightarrow2)\:\dfrac{d}{dx}x^n=nx^{n-1}\\\\:\hookrightarrow3)\:\dfrac{d}{dx}constant=0$