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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of ((e^{x^2}-1))/x

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

integral from 0 to 1 of 1/((x-1)^2)

\int_{0}^{1} \frac{1}{( x - 1 ) ^{2}} d x

taylor (sqrt(1+x))/(sqrt(1-x))taylor

\frac{1 + x}{1 - x}

integral from 0 to 3 of pi(2x)^2

\int_{0}^{3} π (2 x)^{2} d x

integral of 1/((1-y^2)^{1/2)}

\int \frac{1}{( 1 - y ^{2} ) ^{\frac{1}{2}}} d y

Frequently Asked Questions (FAQ)

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