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Popular >

derivative of 1/(1+4x^2)

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (1 + 4 x^{2}) = 8 x

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

Simplify

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

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

Popular Examples

limit as x approaches 0 of (x^2)/(sin^2(7x))

x \to 0 lim (\frac{x ^{2}}{sin ^{2} ( 7 x )})

f (x) = 4 sec (x)

(\partial)/(\partial x)(3sqrt(xy^2-2xy+z))

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

y^{''}-4y^'+7y=0

y^{^{''}} - 4 y^{^{'}} + 7 y = 0

integral from-2 to 3 of (28)/(x^4)

\int_{- 2}^{3} \frac{28}{x ^{4}} d x

Frequently Asked Questions (FAQ)

What is the derivative of 1/(1+4x^2) ?
The derivative of 1/(1+4x^2) is -(8x)/((1+4x^2)^2)
What is the first derivative of 1/(1+4x^2) ?
The first derivative of 1/(1+4x^2) is -(8x)/((1+4x^2)^2)