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

The derivative of 1/(1+2x^2) is -(4x)/((1+2x^2)^2)

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

The first derivative of 1/(1+2x^2) is -(4x)/((1+2x^2)^2)

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (1 + 2 x^{2}) = 4 x

= - \frac{1}{( 1 + 2 x ^{2} ) ^{2}} \cdot 4 x

Simplify

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

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

\frac{4 x ^{3} - 7}{x ^{4}}

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

f (x) = 100 x^{5}

\frac{5}{( s - 3 ) ^{3}}

\int x (x + 5)^{6} d x

What is the derivative of 1/(1+2x^2) ?
The derivative of 1/(1+2x^2) is -(4x)/((1+2x^2)^2)
What is the first derivative of 1/(1+2x^2) ?
The first derivative of 1/(1+2x^2) is -(4x)/((1+2x^2)^2)