What is the derivative of 1/(3sqrt(x^5)) ?

The derivative of 1/(3sqrt(x^5)) is -(5x^4)/(6(x^5)^{3/2)}

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

The first derivative of 1/(3sqrt(x^5)) is -(5x^4)/(6(x^5)^{3/2)}

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derivative of

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

- \frac{5 x ^{4}}{6 ( x ^{5} ) ^{\frac{3}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Simplify

\frac{1}{3} (- \frac{1}{2 ( x ^{5} ) ^{\frac{3}{2}}} \cdot 5 x^{4}) : - \frac{5 x ^{4}}{6 ( x ^{5} ) ^{\frac{3}{2}}}

= - \frac{5 x ^{4}}{6 ( x ^{5} ) ^{\frac{3}{2}}}

\int_{1}^{2} (6 x - 1) d x

f (x) = \frac{2 x}{x + 1}, (1, 1)

\int sin^{5} (4 x) cos^{3} (4 x) d x

f (x) = x^{4} + 2 x

\frac{d ^{2}}{d x ^{2}} (e^{c o s (x)})

What is the derivative of 1/(3sqrt(x^5)) ?
The derivative of 1/(3sqrt(x^5)) is -(5x^4)/(6(x^5)^{3/2)}
What is the first derivative of 1/(3sqrt(x^5)) ?
The first derivative of 1/(3sqrt(x^5)) is -(5x^4)/(6(x^5)^{3/2)}