Question
Differentiate the following functions with respect to x:$\frac{\text{x}}{1+\tan\text{x}}$
✓
Answer
$\frac{\text{d}}{\text{dx}}\Big(\frac{\text{x}}{1+\tan\text{x}}\Big)$$=\frac{(1+\tan\text{x})\frac{\text{d}}{\text{dx}}(\text{x})-\text{x}\frac{\text{d}}{\text{dx}}(1+\tan\text{x})}{(1+\tan\text{x})^2}$
$=\frac{(1+\tan\text{x})-\text{x}(\sec^2\text{x})}{(1+\tan\text{x})^2}$
$=\frac{1+\tan\text{x}-\text{x}\sec^2\text{x}}{(1+\tan\text{x})^2}$
$=\frac{(1+\tan\text{x})-\text{x}(\sec^2\text{x})}{(1+\tan\text{x})^2}$
$=\frac{1+\tan\text{x}-\text{x}\sec^2\text{x}}{(1+\tan\text{x})^2}$
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