Differentiate the following functions with respect to x: (3x+5) - Vidyadip

Question

Differentiate the following functions with respect to x:
$\sin(3\text{x}+5)$

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Answer

Consider $\text{y}=\sin(3\text{x}+5)$
Differentiate y with the respect to x,
$\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\big(\sin(3\text{x}+5)\big)$
$=\cos(3\text{x}+5)\frac{\text{d}}{\text{dx}}(3\text{x}+5)$
[using chain rule]
$=\cos(3\text{x}+5)\times[3(1)+0]$
$=3\cos(3\text{x}+5)$
Hence, the solution is $\frac{\text{d}}{\text{dx}}(\sin(3\text{x}+5))=3\cos(3\text{x}+5)$

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