Find the derivative of the following functions

Question:

Find the derivative of the following functions (it is to be understood that abcdp, q, r and s are fixed non-zero constants and m and n are integers): $\frac{\cos x}{1+\sin x}$

Solution:

Let $f(x)=\frac{\cos x}{1+\sin x}$

By quotient rule,

$f^{\prime}(x)=\frac{(1+\sin x) \frac{d}{d x}(\cos x)-(\cos x) \frac{d}{d x}(1+\sin x)}{(1+\sin x)^{2}}$

$=\frac{(1+\sin x)(-\sin x)-(\cos x)(\cos x)}{(1+\sin x)^{2}}$

$=\frac{-\sin x-\sin ^{2} x-\cos ^{2} x}{(1+\sin x)^{2}}$

$=\frac{-\sin x-\left(\sin ^{2} x+\cos ^{2} x\right)}{(1+\sin x)^{2}}$

$=\frac{-\sin x-1}{(1+\sin x)^{2}}$

$=\frac{-(1+\sin x)}{(1+\sin x)^{2}}$

$=\frac{-1}{(1+\sin x)}$

 

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now