Find the derivative of the following function-fx-a-b sin x-c-d cos x

Here f(x) = a+b sin x/c+d cos x ∴ f'(x)= d/dx [ a+b sin x/c+d cos x ] = (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) ...

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Byju's Answer

Standard XI

Mathematics

Left Hand Derivative

Find the deri...

Question

Find the derivative of the following function:
f(x)= $\frac{a + b s i n x}{c + d c o s x}$

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Solution

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

$∴ f^{'} (x) = \frac{d}{d x} [\frac{a + b s i n x}{c + d c o s x}]$

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

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

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

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

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Find the derivative of the following function: f(x)= a+b sin xc+d cos x

Here f(x)=a+b sin xc+d cos x ∴f′(x)=ddx[a+b sin xc+d cos x] =(c+d cos x)ddx(a+b sin x)−(a+b sin x)ddx(c+d cos x)(c+d cos x)2 =(c+d cos x)(b cos x)−(a+b sin x)(−d sin x)(c+d cos x)2 =bc cos x+ad sin x+bd(cos2 x+sin2x)(c+d cos x)2 =bc cos x+ad sin x+bd(c+d cos x)2

Find the derivative of the following function:
f(x)= $\frac{a + b s i n x}{c + d c o s x}$