What is the derivative of 1/(sqrt(1+x^{12)}) ?

The derivative of 1/(sqrt(1+x^{12)}) is -(6x^{11})/((1+x^{12))^{3/2}}

What is the first derivative of 1/(sqrt(1+x^{12)}) ?

The first derivative of 1/(sqrt(1+x^{12)}) is -(6x^{11})/((1+x^{12))^{3/2}}

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\frac{d}{d x} (\frac{1}{1 + x ^{12}})

- \frac{6 x ^{11}}{( 1 + x ^{12} ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{1 + x ^{12}})

Apply exponent rule:

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

= \frac{d}{d x} ((1 + x^{12})^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 1 + x ^{12} ) ^{\frac{3}{2}}} \frac{d}{d x} (1 + x^{12})

= - \frac{1}{2 ( 1 + x ^{12} ) ^{\frac{3}{2}}} \frac{d}{d x} (1 + x^{12})

\frac{d}{d x} (1 + x^{12}) = 12 x^{11}

= - \frac{1}{2 ( 1 + x ^{12} ) ^{\frac{3}{2}}} \cdot 12 x^{11}

Simplify

- \frac{1}{2 ( 1 + x ^{12} ) ^{\frac{3}{2}}} \cdot 12 x^{11} : - \frac{6 x ^{11}}{( 1 + x ^{12} ) ^{\frac{3}{2}}}

= - \frac{6 x ^{11}}{( 1 + x ^{12} ) ^{\frac{3}{2}}}

\frac{d}{d x} (1 - e^{- 8 x})

2 x + 5 x^{- 1}

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

(\frac{3 y ^{2} - x ^{2}}{y ^{5}}) \frac{d y}{d x} + \frac{x}{2 y ^{4}} = 0

\frac{\partial}{\partial x} (x (x^{2} + 1))

What is the derivative of 1/(sqrt(1+x^{12)}) ?
The derivative of 1/(sqrt(1+x^{12)}) is -(6x^{11})/((1+x^{12))^{3/2}}
What is the first derivative of 1/(sqrt(1+x^{12)}) ?
The first derivative of 1/(sqrt(1+x^{12)}) is -(6x^{11})/((1+x^{12))^{3/2}}