What is the derivative of 5/(xsqrt(x)) ?

The derivative of 5/(xsqrt(x)) is -(15)/(2x^{5/2)}

What is the first derivative of 5/(xsqrt(x)) ?

The first derivative of 5/(xsqrt(x)) is -(15)/(2x^{5/2)}

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\frac{d}{d x} (\frac{5}{x x})

- \frac{15}{2 x ^{\frac{5}{2}}}

Solution steps

\frac{d}{d x} (\frac{5}{x x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (\frac{1}{x x})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

\frac{d}{d x} (x x) = \frac{3 x}{2}

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

Simplify

5 (- \frac{1}{( x x ) ^{2}} \cdot \frac{3 x}{2}) : - \frac{15}{2 x ^{\frac{5}{2}}}

= - \frac{15}{2 x ^{\frac{5}{2}}}

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x^{2} y^{^{''}} + x y^{^{'}} + 25 y = 0

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\int_{- 1}^{1} sec^{3} (x) d x

What is the derivative of 5/(xsqrt(x)) ?
The derivative of 5/(xsqrt(x)) is -(15)/(2x^{5/2)}
What is the first derivative of 5/(xsqrt(x)) ?
The first derivative of 5/(xsqrt(x)) is -(15)/(2x^{5/2)}