Question

Differentiate the function..​

Answer 1

$\frac{d}{dx} ( \frac{2}{ {x}^{ \frac{1}{2} } } + \frac{6}{ {x}^{ \frac{1}{3} } } - \frac{2}{ {x}^{ \frac{3}{2} } } - \frac{4}{ {x}^{ \frac{3}{4} } } ) \\ = 2( \frac{d}{dx} ( {x}^{ - \frac{1}{2} } )) + 6( \frac{d}{dx} ( {x}^{ - \frac{1}{3} } )) - 2( \frac{d}{dx} ( {x}^{ - \frac{3}{2} } )) - 4( \frac{d}{dx} ( {x}^{ - \frac{3}{4} } )) \\ =( 2 \times - \frac{ 1}{2} {x}^{ - \frac{ 3}{4} } ) +( 6\times - \frac{ 1}{3} {x}^{ - \frac{ 4}{3} } ) - ( 2 \times - \frac{ 3}{2} {x}^{ - \frac{ 5}{2} } ) - ( 4 \times - \frac{ 3}{4} {x}^{ - \frac{ 7}{4} } ) \\ = - {x}^{ - \frac{3}{4} } - 2. {x}^{ - \frac{4}{3} } + 3. {x}^{ - \frac{5}{2} } + 3. {x}^{ - \frac{7}{4} }$

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