What is the derivative of 1/(sqrt(x^{13)}) ?

The derivative of 1/(sqrt(x^{13)}) is -(13)/(2x^{15/2)}

What is the first derivative of 1/(sqrt(x^{13)}) ?

The first derivative of 1/(sqrt(x^{13)}) is -(13)/(2x^{15/2)}

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\frac{d}{d x} (\frac{1}{x ^{13}})

- \frac{13}{2 x ^{\frac{15}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{13}})

Apply exponent rule:

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

= \frac{d}{d x} ((x^{13})^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x ^{13} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{13})

= - \frac{1}{2 ( x ^{13} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{13})

\frac{d}{d x} (x^{13}) = 13 x^{12}

= - \frac{1}{2 ( x ^{13} ) ^{\frac{3}{2}}} \cdot 13 x^{12}

Simplify

- \frac{1}{2 ( x ^{13} ) ^{\frac{3}{2}}} \cdot 13 x^{12} : - \frac{13}{2 x ^{\frac{15}{2}}}

= - \frac{13}{2 x ^{\frac{15}{2}}}

\int 4 tan^{3} (x) sec (x) d x

\int_{- 1}^{0} (x + 1)^{3} d x

\frac{d}{d x} (7 x - 4)

(y^{3} - 1) e x d x + 3 y^{2} (e x + 1) d y = 0

x \to 0 lim (4 x cot (x))

What is the derivative of 1/(sqrt(x^{13)}) ?
The derivative of 1/(sqrt(x^{13)}) is -(13)/(2x^{15/2)}
What is the first derivative of 1/(sqrt(x^{13)}) ?
The first derivative of 1/(sqrt(x^{13)}) is -(13)/(2x^{15/2)}