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Popular Calculus >

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

Solution

derivative of

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

Solution

- \frac{16}{( 4 x + 1 ) ^{5}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{4}{( 4 x + 1 ) ^{5}} \frac{d}{d x} (4 x + 1)

= - \frac{4}{( 4 x + 1 ) ^{5}} \frac{d}{d x} (4 x + 1)

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

= - \frac{4}{( 4 x + 1 ) ^{5}} \cdot 4

Simplify

- \frac{4}{( 4 x + 1 ) ^{5}} \cdot 4 : - \frac{16}{( 4 x + 1 ) ^{5}}

= - \frac{16}{( 4 x + 1 ) ^{5}}

Graph

Popular Examples

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x \to 3 - lim (\frac{x - 2}{x ^{2} - 9})

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\frac{d}{d x} (arccsc (- 3 x))

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\frac{d}{d x} (arctan (\frac{t}{x}))

derivative of (2x-4/(3e^x))

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

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x \to 3 lim (\frac{1}{( x ^{2} - 9 )})

Frequently Asked Questions (FAQ)

What is the derivative of 1/((4x+1)^4) ?
The derivative of 1/((4x+1)^4) is -(16)/((4x+1)^5)
What is the first derivative of 1/((4x+1)^4) ?
The first derivative of 1/((4x+1)^4) is -(16)/((4x+1)^5)