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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of 750+12x-0.08x^7

\frac{d}{d x} (750 + 12 x - 0.08 x^{7})

derivative of x^4+8x+6 derivative of

x^{4} + 8 x + 6

derivative of (3-x^2(x^3-x+1))

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

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

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

integral of (x^4+x^3+x^2+1)/(x^2+x-2)

\int \frac{x ^{4} + x ^{3} + x ^{2} + 1}{x ^{2} + x - 2} d x

Frequently Asked Questions (FAQ)

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