If y -2-3 cos x -sin x- find dy - dx at x -4

We have, y= 2 3cosx/sinx dy/dx= d/dx ( 2 3cosx/sinx ) = d/dx(2cosecx=3cosx) =2 d/dx(cosecx) 33 d/dx(cotx) = 2 cosecx . cotx +3 cosec^2x dy/dx at x= π/4 ...

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Byju's Answer

Standard XII

Mathematics

Algebra of Derivatives

If y =2-3 cos...

Question

If $y = (\frac{2 - 3 c o s x}{s i n x}),$ find $\frac{d y}{d x}$ at $x = \frac{π}{4}$

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Solution

We have,

$y = \frac{2 - 3 c o s x}{s i n x}$

$\frac{d y}{d x} = \frac{d}{d x} (\frac{2 - 3 c o s x}{s i n x})$

$= \frac{d}{d x} (2 c o s e c x = 3 c o s x)$

$= 2 \frac{d}{d x} (c o s e c x) - 33 \frac{d}{d x} (c o t x)$

$= - 2 c o s e c x . c o t x + 3 c o s e c^{2} x \frac{d y}{d x}$ at $x = \frac{π}{4}$

$= - 2 c o s e c \frac{π}{4} . c o t \frac{π}{4} + 3 c o s e c^{2} \frac{π}{4}$

$= - 2 \sqrt{2} - 1 + 3.2$

$= - 2 \sqrt{2} + 6$

$= 6 - 2 \sqrt{2}$

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If y=(2−3cosxsinx), find dydx at x=π4

We have, y=2−3cosxsinx dydx=ddx(2−3cosxsinx) =ddx(2cosecx=3cosx) =2ddx(cosecx)−33ddx(cotx) =−2cosecx.cotx+3cosec2xdydx at x=π4 =−2cosecπ4.cotπ4+3cosec2π4 =−2√2−1+3.2 =−2√2+6 =6−2√2

If $y = (\frac{2 - 3 c o s x}{s i n x}),$ find $\frac{d y}{d x}$ at $x = \frac{π}{4}$