Question

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): cosx / (1+sinx)

Answer 1

Answer:

given:

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

d.w.r to x

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

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

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

$f'(x) = \frac{cos\ x(-cos\ x) - [(1 - sin\ x)(-sin\ x)]}{cos^2x}$

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

$f'(x) = tan\ x\ sec\ x \ - \ sec^2x$