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Popular >

derivative of 1/(4x-1)

Solution

\frac{d}{d x} (\frac{1}{4 x - 1})

Solution

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

Solution steps

\frac{d}{d x} (\frac{1}{4 x - 1})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

Frequently Asked Questions (FAQ)

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