What is the derivative of f(x)=sqrt(1/(x^{31))} ?

The derivative of f(x)=sqrt(1/(x^{31))} is -(31sqrt(x^{30)})/(2x^{63/2)}

What is the first derivative of f(x)=sqrt(1/(x^{31))} ?

The first derivative of f(x)=sqrt(1/(x^{31))} is -(31sqrt(x^{30)})/(2x^{63/2)}

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derivative of

f (x) = \frac{1}{x ^{31}}

- \frac{31 x ^{30}}{2 x ^{\frac{63}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{31}})

Apply the chain rule:

\frac{1}{2 \frac{1}{x ^{31}}} \frac{d}{d x} (\frac{1}{x ^{31}})

= \frac{1}{2 \frac{1}{x ^{31}}} \frac{d}{d x} (\frac{1}{x ^{31}})

\frac{d}{d x} (\frac{1}{x ^{31}}) = - \frac{31}{x ^{32}}

= \frac{1}{2 \frac{1}{x ^{31}}} (- \frac{31}{x ^{32}})

Simplify

\frac{1}{2 \frac{1}{x ^{31}}} (- \frac{31}{x ^{32}}) : - \frac{31 x ^{30}}{2 x ^{\frac{63}{2}}}

= - \frac{31 x ^{30}}{2 x ^{\frac{63}{2}}}

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

x \to 4 lim (3 x^{3} - 2 x^{2} + x - 7)

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

\int \frac{3 - 18 x}{25 - 9 x ^{2}} d x

ln (\frac{4 x}{x + 7})

What is the derivative of f(x)=sqrt(1/(x^{31))} ?
The derivative of f(x)=sqrt(1/(x^{31))} is -(31sqrt(x^{30)})/(2x^{63/2)}
What is the first derivative of f(x)=sqrt(1/(x^{31))} ?
The first derivative of f(x)=sqrt(1/(x^{31))} is -(31sqrt(x^{30)})/(2x^{63/2)}