Differentiate the following functions with respect to x -a-sin x-1-a sin x

We have, d/dx(a+sin x/1+a sin x ) Using quotient rule, we get (1+a sin x)d/dx(a+sin x) (a+sin x)d/dx(1+a sin x)/(1+a sin x)^2 =(1+a sin x)cos x (a+sin x)a 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 :

$\frac{a + s i n x}{1 + a s i n x}$

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Solution

We have,

$\frac{d}{d x} (\frac{a + s i n x}{1 + a s i n x})$

Using quotient rule, we get

$\frac{(1 + a s i n x) \frac{d}{d x} (a + s i n x) - (a + s i n x) \frac{d}{d x} (1 + a s i n x)}{(1 + a s i n x)^{2}}$

$= \frac{(1 + a s i n x) c o s x - (a + s i n x) a c o s x}{(1 + a s i n x)^{2}} = \frac{c o s x + a s i n x c o s x - a^{2} c o s x - a s i n x c o s x}{(1 + a s i n x)^{2}}$

$= \frac{(1 - a^{2}) c o s x}{(1 + a s i n x)^{2}}$

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