Differentiate the following equation-x2cos-4-sin x

X^2 cos π/4/sin x We have, d/dx ( x^2 cos π/4× cosec x ) = cos π/4 cosec x d/dx(x^2) +x^2 cosec x d/dx ( cos π/4 ) +x^2 cosπ/4d/dx (cosecx) [Using ...

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Byju's Answer

Standard XII

Mathematics

Product Rule of Differentiation

Differentiate...

Question

Differentiate the following equation:
$\frac{x^{2} c o s \frac{π}{4}}{s i n x}$

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Solution

$\frac{x^{2} c o s \frac{π}{4}}{s i n x}$

We have,

$\frac{d}{d x} (x^{2} c o s \frac{π}{4} \times c o s e c x)$

$= c o s \frac{π}{4} c o s e c x \frac{d}{d x} (x^{2}) + x^{2} c o s e c x \frac{d}{d x} (c o s \frac{π}{4}) + x^{2} c o s \frac{π}{4} \frac{d}{d x} (c o s e c x)$ [Using product rule]

$= c o s \frac{π}{4} c o s e c x \times 2 x + x^{2} c o s e c x \times 0 + x^{2} c o s \frac{π}{4} (- c o s e c x c o t x) .$ $[∵ \frac{d}{d x} (c o s \frac{π}{4}) = 0]$

$= (\frac{2 x}{s i n x} - \frac{x^{2} c o s e c x}{s i n^{2} x}) c o s \frac{π}{4}$

$∴ c o s \frac{π}{4} (\frac{2 x}{s i n x} - \frac{x^{2} c o s x}{s i n x})$

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Differentiate the following equation: x2 cos π4sin x

x2 cos π4sin x We have, ddx(x2 cosπ4×cosec x) =cos π4 cosec x ddx(x2)+x2 cosec x ddx(cosπ4)+x2 cosπ4ddx(cosecx) [Using product rule] =cosπ4 cosecx×2x+x2 cosec x×0+x2 cosπ4(−cosecx cotx). [∵ddx(cosπ4)=0] =(2xsin x−x2 cosecxsin2x)cosπ4 ∴cos π4(2xsin x−x2 cos xsin x)

Differentiate the following equation:
$\frac{x^{2} c o s \frac{π}{4}}{s i n x}$