What is the derivative of f(x)= 1/(6sqrt(x^3)) ?

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

What is the first derivative of f(x)= 1/(6sqrt(x^3)) ?

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

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derivative of

f (x) = \frac{1}{6 x ^{3}}

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

Solution steps

\frac{d}{d x} (\frac{1}{6 x ^{3}})

Take the constant out:

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

= \frac{1}{6} \frac{d}{d x} (\frac{1}{x ^{3}})

Apply exponent rule:

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

= \frac{1}{6} \frac{d}{d x} ((x^{3})^{- \frac{1}{2}})

Apply the chain rule:

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

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

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

= \frac{1}{6} (- \frac{1}{2 ( x ^{3} ) ^{\frac{3}{2}}} \cdot 3 x^{2})

Simplify

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

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

f (x) = \frac{2}{x - 6}, at x = 8

\int_{2}^{5} \frac{x}{x ^{2} + 4 x + 20} d x

(x^{2} - 16 x + 64) (x^{2} + 64 x + 4)

\int \frac{sec ( \frac{1}{x} )}{x ^{2}} d x

\frac{d y}{d x} = (\frac{x - y}{x})

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