What is the derivative of 1/(sqrt(1+5x^2)) ?

The derivative of 1/(sqrt(1+5x^2)) is -(5x)/((1+5x^2)^{3/2)}

What is the first derivative of 1/(sqrt(1+5x^2)) ?

The first derivative of 1/(sqrt(1+5x^2)) is -(5x)/((1+5x^2)^{3/2)}

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\frac{d}{d x} (\frac{1}{1 + 5 x ^{2}})

- \frac{5 x}{( 1 + 5 x ^{2} ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{1 + 5 x ^{2}})

Apply exponent rule:

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

= \frac{d}{d x} ((1 + 5 x^{2})^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 1 + 5 x ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (1 + 5 x^{2})

= - \frac{1}{2 ( 1 + 5 x ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (1 + 5 x^{2})

\frac{d}{d x} (1 + 5 x^{2}) = 10 x

= - \frac{1}{2 ( 1 + 5 x ^{2} ) ^{\frac{3}{2}}} \cdot 10 x

Simplify

- \frac{1}{2 ( 1 + 5 x ^{2} ) ^{\frac{3}{2}}} \cdot 10 x : - \frac{5 x}{( 1 + 5 x ^{2} ) ^{\frac{3}{2}}}

= - \frac{5 x}{( 1 + 5 x ^{2} ) ^{\frac{3}{2}}}

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What is the derivative of 1/(sqrt(1+5x^2)) ?
The derivative of 1/(sqrt(1+5x^2)) is -(5x)/((1+5x^2)^{3/2)}
What is the first derivative of 1/(sqrt(1+5x^2)) ?
The first derivative of 1/(sqrt(1+5x^2)) is -(5x)/((1+5x^2)^{3/2)}