What is the derivative of 1/(sqrt(1+x^8)) ?

The derivative of 1/(sqrt(1+x^8)) is -(4x^7)/((1+x^8)^{3/2)}

What is the first derivative of 1/(sqrt(1+x^8)) ?

The first derivative of 1/(sqrt(1+x^8)) is -(4x^7)/((1+x^8)^{3/2)}

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\frac{d}{d x} (\frac{1}{1 + x ^{8}})

- \frac{4 x ^{7}}{( 1 + x ^{8} ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{1 + x ^{8}})

Apply exponent rule:

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

= \frac{d}{d x} ((1 + x^{8})^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 1 + x ^{8} ) ^{\frac{3}{2}}} \frac{d}{d x} (1 + x^{8})

= - \frac{1}{2 ( 1 + x ^{8} ) ^{\frac{3}{2}}} \frac{d}{d x} (1 + x^{8})

\frac{d}{d x} (1 + x^{8}) = 8 x^{7}

= - \frac{1}{2 ( 1 + x ^{8} ) ^{\frac{3}{2}}} \cdot 8 x^{7}

Simplify

- \frac{1}{2 ( 1 + x ^{8} ) ^{\frac{3}{2}}} \cdot 8 x^{7} : - \frac{4 x ^{7}}{( 1 + x ^{8} ) ^{\frac{3}{2}}}

= - \frac{4 x ^{7}}{( 1 + x ^{8} ) ^{\frac{3}{2}}}

\int 6 e^{- 0.5 x} d x

\frac{\partial}{\partial x} (ln (5 x^{2} - 2 y^{2}))

\int_{1}^{3} \frac{2}{4 + ( x - 1 ) ^{2}} d x

y^{^{'}} = \frac{2 y}{x}

x \to 0 lim (\frac{x ^{2}}{x})

What is the derivative of 1/(sqrt(1+x^8)) ?
The derivative of 1/(sqrt(1+x^8)) is -(4x^7)/((1+x^8)^{3/2)}
What is the first derivative of 1/(sqrt(1+x^8)) ?
The first derivative of 1/(sqrt(1+x^8)) is -(4x^7)/((1+x^8)^{3/2)}