Question
Differentiate the following functions with respect to x:
$\tan^2\text{x}$
$\tan^2\text{x}$
✓
Answer
Let,
$\text{y}=\tan^2\text{x}$
Differentiate it with respect to x,
$\frac{\text{dy}}{\text{dx}}=2\tan\text{x }\frac{\text{d}}{\text{dx}}(\tan\text{x})\ \big[\text{using chain rule}\big]$
$=2\tan\text{x}\times\sec^2\text{x}$
So,
$\frac{\text{d}}{\text{dx}}=\big(\tan^2\text{x}\big)=2\tan\text{x }\sec^2\text{x}.$
$\text{y}=\tan^2\text{x}$
Differentiate it with respect to x,
$\frac{\text{dy}}{\text{dx}}=2\tan\text{x }\frac{\text{d}}{\text{dx}}(\tan\text{x})\ \big[\text{using chain rule}\big]$
$=2\tan\text{x}\times\sec^2\text{x}$
So,
$\frac{\text{d}}{\text{dx}}=\big(\tan^2\text{x}\big)=2\tan\text{x }\sec^2\text{x}.$
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