What is the derivative of ((1))/((x^n+a^n)) ?

The derivative of ((1))/((x^n+a^n)) is -(nx^{n-1})/((x^n+a^n)^2)

What is the first derivative of ((1))/((x^n+a^n)) ?

The first derivative of ((1))/((x^n+a^n)) is -(nx^{n-1})/((x^n+a^n)^2)

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derivative of

\frac{( 1 )}{( x ^{n} + a ^{n} )}

- \frac{n x ^{n - 1}}{( x ^{n} + a ^{n} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{n} + a ^{n}})

Apply exponent rule:

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

= \frac{d}{d x} ((x^{n} + a^{n})^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{n} + a ^{n} ) ^{2}} \frac{d}{d x} (x^{n} + a^{n})

= - \frac{1}{( x ^{n} + a ^{n} ) ^{2}} \frac{d}{d x} (x^{n} + a^{n})

\frac{d}{d x} (x^{n} + a^{n}) = n x^{n - 1}

= - \frac{1}{( x ^{n} + a ^{n} ) ^{2}} n x^{n - 1}

Simplify

- \frac{1}{( x ^{n} + a ^{n} ) ^{2}} n x^{n - 1} : - \frac{n x ^{n - 1}}{( x ^{n} + a ^{n} ) ^{2}}

= - \frac{n x ^{n - 1}}{( x ^{n} + a ^{n} ) ^{2}}

What is the derivative of ((1))/((x^n+a^n)) ?
The derivative of ((1))/((x^n+a^n)) is -(nx^{n-1})/((x^n+a^n)^2)
What is the first derivative of ((1))/((x^n+a^n)) ?
The first derivative of ((1))/((x^n+a^n)) is -(nx^{n-1})/((x^n+a^n)^2)