Differentiate w.r.t. x the function in Exercise: ^3x+ ^6x - Vidyadip

Question

Differentiate w.r.t. x the function in Exercise:
$\sin^3\text{x}+\cos^6\text{x}$

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Answer

Let $\text{y}=\sin^3\text{x}+\cos^6\text{x}$$\therefore\ \frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}(\sin^3\text{x})+\frac{\text{d}}{\text{dx}}(\cos^6\text{x})$
$=3\sin^2\text{x}.\frac{\text{d}}{\text{dx}}(\sin\text{x})+6\cos^5\text{x}.\frac{\text{d}}{\text{dx}}(\cos\text{x})$
$=3\sin^2\text{x}.\cos\text{x}+6\cos^5\text{x}.(-\sin\text{x})$
$=3\sin\text{x}\cos\text{x}(\sin\text{x}-2\cos^4\text{x})$

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