What is the derivative of 1/(sqrt(x^5)) ?

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

What is the first derivative of 1/(sqrt(x^5)) ?

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

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derivative of

\frac{1}{x ^{5}}

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

Simplify

- \frac{1}{2 ( x ^{5} ) ^{\frac{3}{2}}} \cdot 5 x^{4} : - \frac{5 x ^{4}}{2 ( x ^{5} ) ^{\frac{3}{2}}}

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

\int - sec^{2} (x) + cos (2 x) d x

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

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

\frac{2 u ^{2}}{( u ^{2} + u ) ^{3}}

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

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