What is the derivative of 1/(sqrt(x^{15)}) ?

The derivative of 1/(sqrt(x^{15)}) is -(15)/(2x^{17/2)}

What is the first derivative of 1/(sqrt(x^{15)}) ?

The first derivative of 1/(sqrt(x^{15)}) is -(15)/(2x^{17/2)}

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\frac{d}{d x} (\frac{1}{x ^{15}})

- \frac{15}{2 x ^{\frac{17}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{15}})

Apply exponent rule:

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

= \frac{d}{d x} ((x^{15})^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x ^{15} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{15})

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

\frac{d}{d x} (x^{15}) = 15 x^{14}

= - \frac{1}{2 ( x ^{15} ) ^{\frac{3}{2}}} \cdot 15 x^{14}

Simplify

- \frac{1}{2 ( x ^{15} ) ^{\frac{3}{2}}} \cdot 15 x^{14} : - \frac{15}{2 x ^{\frac{17}{2}}}

= - \frac{15}{2 x ^{\frac{17}{2}}}

\frac{1}{14 x ^{2}}, x, \frac{x}{4}

\int x^{2} - x^{3} d x

\int_{0}^{1} \frac{1}{3 x} d x

\int_{0}^{25} (- 6 x) d x

x \to 2 lim (x^{3} - 5 x^{2} + 1)

What is the derivative of 1/(sqrt(x^{15)}) ?
The derivative of 1/(sqrt(x^{15)}) is -(15)/(2x^{17/2)}
What is the first derivative of 1/(sqrt(x^{15)}) ?
The first derivative of 1/(sqrt(x^{15)}) is -(15)/(2x^{17/2)}