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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int t^{3} ln (t) d t

\int sin (m x) sin (n x) d x

y = \frac{8 x ^{2} + 2 x + 6}{x}

\frac{d}{d x} (1000 x e^{- 0.5 x})

\frac{\partial}{\partial x} (z^{3} ln (x y))

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