Find the derivative of the following function-fx-4 x-5 sin x-3 x-7 cos x

Here f(x)= 4x+5 sin x/3x+7 cos x ∴ f'(x)= d/dx [ 4x+5 sin x/3x+7 cos x ] = (3x+7 cos x)d/dx(4x+5 sin x) (4x+5 sin x)d/dx(3x+7 cos x)/(3x+7 cos x)^2 = (3x+7 c ...

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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)= $\frac{4 x + 5 s i n x}{3 x + 7 c o s x}$

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Solution

Here $f (x) = \frac{4 x + 5 s i n x}{3 x + 7 c o s x}$

$∴ f^{'} (x) = \frac{d}{d x} [\frac{4 x + 5 s i n x}{3 x + 7 c o s x}]$

$= \frac{(3 x + 7 c o s x) \frac{d}{d x} (4 x + 5 s i n x) - (4 x + 5 s i n x) \frac{d}{d x} (3 x + 7 c o s x)}{(3 x + 7 c o s x)^{2}}$

$= \frac{(3 x + 7 c o s x) (4 + 5 c o s x) - (4 x + 5 s i n x) (3 - 7 s i n x)}{(3 x + 7 c o s x)^{2}}$

$= \frac{12 x + 15 x c o s x + 28 c o s x + 35 c o s^{2} x - 12 x + 28 x s i n x - 15 s i n x + 35 s i n^{2} x}{(3 x + 7 c o s x)^{2}}$

$= \frac{15 x c o s x + 28 c o s x + 28 x s i n x - 15 s i n x + 35 (c o s^{2} x + s i n^{2} x)}{(3 x + 7 c o s x)^{2}}$

$= \frac{15 x c o s x + 28 c o s x + 28 x s i n x - 15 s i n x + 35}{(3 x + 7 c o s x)^{2}}$

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Find the derivative of the following function: f(x)= 4x+5 sin x3x+7 cos x

Find the derivative of the following function:
f(x)= $\frac{4 x + 5 s i n x}{3 x + 7 c o s x}$