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Popular >

derivative of 1/((1+2x^2))

Solution

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

Solution

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

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})

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial z)(4xy^3(z^2+1)^3)

\frac{\partial}{\partial z} (4 x y^{3} (z^{2} + 1)^{3})

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Frequently Asked Questions (FAQ)

What is the derivative of 1/((1+2x^2)) ?
The derivative of 1/((1+2x^2)) is -4/((1+2x)^3)
What is the first derivative of 1/((1+2x^2)) ?
The first derivative of 1/((1+2x^2)) is -4/((1+2x)^3)