Differentiate the following functions with respect to x -a-b sin x-c-d cos x

Let y = a+b sin x/c+d cos x Differentiating y w.r.t., we get dy/dx=(c+d cos x)d/dx(a+b sin x) (a+b sin x)d/dx(c+d cos x)/(c+d cos x)^2 =(c+d cos x)[0+b cos x] ( ...

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Byju's Answer

Standard XII

Mathematics

Quotient Rule of Differentiation

Differentiate...

Question

Differentiate the following functions with respect to x :

$\frac{a + b s i n x}{c + d c o s x}$

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Solution

Let y = $\frac{a + b s i n x}{c + d c o s x}$

Differentiating y w.r.t., we get

$\frac{d y}{d x} = \frac{(c + d c o s x) \frac{d}{d x} (a + b s i n x) - (a + b s i n x) \frac{d}{d x} (c + d c o s x)}{(c + d c o s x)^{2}}$

$= \frac{(c + d c o s x) [0 + b c o s x] - (a + b s i n x) (0 - d s i n x)}{(c + d c o s x)^{2}}$

$= \frac{(c + d c o s x) (b c o s x) - (a + b s i n x) (- d s i n x)}{(c + d c o s x)^{2}}$

$= \frac{b c c o s x + b d c o s^{2} x + a d s i n x + b d s i n^{2} x}{(c + d c o s x)^{2}}$

$= \frac{b c c o s x + a d s i n x + b d (c o s^{2} x + s i n^{2} x)}{(c + d c o s x)^{2}}$

$\Rightarrow \frac{d y}{d x} = \frac{b c c o s x + a d s i n x + b d}{(c + d c o s x)^{2}}$

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Differentiate the following functions with respect to x : a+b sin xc+d cos x

Differentiate the following functions with respect to x :

$\frac{a + b s i n x}{c + d c o s x}$