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Popular >

derivative of 1/(5x+1)

Solution

\frac{d}{d x} (\frac{1}{5 x + 1})

Solution

- \frac{5}{( 5 x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{5 x + 1})

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{1}{( 5 x + 1 ) ^{2}} \frac{d}{d x} (5 x + 1)

= - \frac{1}{( 5 x + 1 ) ^{2}} \frac{d}{d x} (5 x + 1)

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

= - \frac{1}{( 5 x + 1 ) ^{2}} \cdot 5

Simplify

- \frac{1}{( 5 x + 1 ) ^{2}} \cdot 5 : - \frac{5}{( 5 x + 1 ) ^{2}}

= - \frac{5}{( 5 x + 1 ) ^{2}}

Popular Examples

integral of (3-18x)/(sqrt(49-9x^2))

\int \frac{3 - 18 x}{49 - 9 x ^{2}} d x

derivative of sqrt(3x^2-5)

\frac{d}{d x} (3 x^{2} - 5)

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

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

limit as x approaches-1f of x

x \to - 1 f lim (x)

area g(x)=x^2,g(x)=x^k0,1 area

g (x) = x^{2}, g (x) = x^{k} 0, 1

Frequently Asked Questions (FAQ)

What is the derivative of 1/(5x+1) ?
The derivative of 1/(5x+1) is -5/((5x+1)^2)
What is the first derivative of 1/(5x+1) ?
The first derivative of 1/(5x+1) is -5/((5x+1)^2)