Differentiate the following functions with respect to x -4 x-5 sin x-3 x-7 cos x

Let y=4x+5 sin x/3x+7 cos x Differentiating y w.r.t. x, we get dy/dx=(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 (By quotient for ...

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Byju's Answer

Standard XII

Mathematics

Quotient Rule of Differentiation

Differentiate...

Question

Differentiate the following functions with respect to x :

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

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Solution

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

Differentiating y w.r.t. x, we get

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

$= \frac{(3 x + 7 c o s x) (4 \times 1 + 5 c o s x) - (4 x + 5 s i n x) (3 - 7 s i n x)}{(3 x + 7 c o s x)^{2}}$

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

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

$= \frac{35 + 15 x c o s x + 28 c o s x + 28 x s i n x - 15 s i n x}{(3 x + 7 c o s x)^{2}} [∵ s i n^{2} x + c o s^{2} = 1]$

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Differentiate the following functions with respect to x : 4x+5 sin x3x+7 cos x

Differentiate the following functions with respect to x :

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