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Problem If y = 2 ( x − sin x ) 3 / 2 x y = \frac{2(x - \sin x)^{3/2}}{\sqrt{x}} y = x 2 ( x − s i n x ) 3/2 d y d x = \frac{dy}{dx} = d x d y = 2 ( x − sin x ) 3 / 2 x [ 3 2 1 − cos x 1 − sin x − 1 2 x ] \frac{2(x - \sin x)^{3/2}}{\sqrt{x}} \left[ \frac{3}{2} \frac{1 - \cos x}{1 - \sin x} - \frac{1}{2x} \right] x 2 ( x − s i n x ) 3/2 [ 2 3 1 − s i n x 1 − c o s x − 2 x 1 ] 2 ( x − sin x ) 3 / 2 x [ 3 2 1 − cos x x − sin x − 1 2 x ] \frac{2(x - \sin x)^{3/2}}{\sqrt{x}} \left[ \frac{3}{2} \frac{1 - \cos x}{x - \sin x} - \frac{1}{2x} \right] x 2 ( x − s i n x ) 3/2 [ 2 3 x − s i n x 1 − c o s x − 2 x 1 ] 2 ( x − sin x ) 1 / 2 x [ 3 2 1 − cos x x − sin x − 1 2 x ] \frac{2(x - \sin x)^{1/2}}{\sqrt{x}} \left[ \frac{3}{2} \frac{1 - \cos x}{x - \sin x} - \frac{1}{2x} \right] x 2 ( x − s i n x ) 1/2 [ 2 3 x − s i n x 1 − c o s x − 2 x 1 ] Browse the problem library