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

We have, d/dx(a cos x+b sin x+c/sin x ) =ad/dx(cos x/sin x)+bd/dx(1)+cd/dx(1/sin x ) =a( cosec^2x)+0+c( cosec x.cot x) = a cosec^2x c cosec x.cot x ...

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Byju's Answer

Standard XII

Mathematics

Addition Rule of Differentiation

Differentiate...

Question

Differentiate the following functions with respect to x :

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

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Solution

We have,

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

$= a \frac{d}{d x} (\frac{c o s x}{s i n x}) + b \frac{d}{d x} (1) + c \frac{d}{d x} (\frac{1}{s i n x})$

$= a (- c o s e c^{2} x) + 0 + c (- c o s e c x . c o t x) = - a c o s e c^{2} x - c c o s e c x . c o t x$

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

We have, ddx(a cos x+b sin x+csin x) =addx(cos xsin x)+bddx(1)+cddx(1sin x) =a(−cosec2x)+0+c(−cosec x.cot x)=−a cosec2x−c cosec x.cot x

Differentiate the following functions with respect to x :

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

We have,

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

$= a \frac{d}{d x} (\frac{c o s x}{s i n x}) + b \frac{d}{d x} (1) + c \frac{d}{d x} (\frac{1}{s i n x})$

$= a (- c o s e c^{2} x) + 0 + c (- c o s e c x . c o t x) = - a c o s e c^{2} x - c c o s e c x . c o t x$