Find the derivative of the following function-fx-x2cos-4-sin x

Here, f(x)= x^2 cos ( π/4 )/sin x ∴ f'(x)= d/dx [ x^2 cos ( π/4 )/sin x ] = sin x d/dx [ x^2 cos ( π/4 ) ] x^2 cos (π/4)(d/dx(sin x) )/sin^2 x = sin x ...

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

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Solution

Here, $f (x) = \frac{x^{2} c o s (\frac{π}{4})}{s i n x}$

$∴ f^{'} (x) = \frac{d}{d x} [\frac{x^{2} c o s (\frac{π}{4})}{s i n x}]$

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

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

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

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

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Find the derivative of the following function: f(x) = x2 cos (π4)sin x

Here, f(x)=x2 cos (π4)sin x ∴f′(x)=ddx[x2 cos (π4)sin x] =sin x ddx[x2 cos(π4)]−x2 cos(π4)(ddx(sin x))sin2 x =sin x [2x cos (π4)]−x2 cos(π4)(cos x)sin2x =2x sin x cos(π4)−x2 cos x cos (π4)sin2x =x cos (π4)[2 sin x−x cos x]sin2x

Find the derivative of the following function:
f(x) = $\frac{x^{2} c o s (\frac{π}{4})}{s i n x}$