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Popular >

derivative of 1/(5x+2)

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of (ln(3x))^2 derivative of

(ln (3 x))^{2}

integral from-1 to 3 of x^3+2x-5

\int_{- 1}^{3} x^{3} + 2 x - 5 d x

(\partial)/(\partial x)(1x+14y)

\frac{\partial}{\partial x} (1 x + 14 y)

derivative of 2+x^4

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

derivative of-7x^9

\frac{d}{d x} (- 7 x^{9})

Frequently Asked Questions (FAQ)

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