What is the derivative of 1/(2sqrt(x))-5/(2x^{3/2)} ?

The derivative of 1/(2sqrt(x))-5/(2x^{3/2)} is -1/(4x^{3/2)}+(15)/(4x^{5/2)}

What is the first derivative of 1/(2sqrt(x))-5/(2x^{3/2)} ?

The first derivative of 1/(2sqrt(x))-5/(2x^{3/2)} is -1/(4x^{3/2)}+(15)/(4x^{5/2)}

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derivative of

\frac{1}{2 x} - \frac{5}{2 x ^{\frac{3}{2}}}

- \frac{1}{4 x ^{\frac{3}{2}}} + \frac{15}{4 x ^{\frac{5}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{2 x} - \frac{5}{2 x ^{\frac{3}{2}}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{1}{2 x}) - \frac{d}{d x} (\frac{5}{2 x ^{\frac{3}{2}}})

\frac{d}{d x} (\frac{1}{2 x}) = - \frac{1}{4 x ^{\frac{3}{2}}}

\frac{d}{d x} (\frac{5}{2 x ^{\frac{3}{2}}}) = - \frac{15}{4 x ^{\frac{5}{2}}}

= - \frac{1}{4 x ^{\frac{3}{2}}} - (- \frac{15}{4 x ^{\frac{5}{2}}})

Simplify

= - \frac{1}{4 x ^{\frac{3}{2}}} + \frac{15}{4 x ^{\frac{5}{2}}}

d er i v a t i v e f (x) = \frac{x}{x + \frac{a}{x}}

\int e^{x} + sin (x) d x

d er i v a t i v e y = \frac{2 x ^{2} + 2 x + 4}{x}

\int \frac{10}{x ^{3}} d x

\int \frac{2 x - 1}{x} d x

What is the derivative of 1/(2sqrt(x))-5/(2x^{3/2)} ?
The derivative of 1/(2sqrt(x))-5/(2x^{3/2)} is -1/(4x^{3/2)}+(15)/(4x^{5/2)}
What is the first derivative of 1/(2sqrt(x))-5/(2x^{3/2)} ?
The first derivative of 1/(2sqrt(x))-5/(2x^{3/2)} is -1/(4x^{3/2)}+(15)/(4x^{5/2)}