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Popular >

derivative of 1/(2x+9)

Solution

\frac{d}{d x} (\frac{1}{2 x + 9})

Solution

- \frac{2}{( 2 x + 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{2 x + 9})

Apply exponent rule:

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

= \frac{d}{d x} ((2 x + 9)^{- 1})

Apply the chain rule:

- \frac{1}{( 2 x + 9 ) ^{2}} \frac{d}{d x} (2 x + 9)

= - \frac{1}{( 2 x + 9 ) ^{2}} \frac{d}{d x} (2 x + 9)

\frac{d}{d x} (2 x + 9) = 2

= - \frac{1}{( 2 x + 9 ) ^{2}} \cdot 2

Simplify

- \frac{1}{( 2 x + 9 ) ^{2}} \cdot 2 : - \frac{2}{( 2 x + 9 ) ^{2}}

= - \frac{2}{( 2 x + 9 ) ^{2}}

Popular Examples

integral from 1 to 4 of (2x+1)

\int_{1}^{4} (2 x + 1) d x

(\partial)/(\partial x)((2s-3x)/(3s+5x))

\frac{\partial}{\partial x} (\frac{2 s - 3 x}{3 s + 5 x})

limit as x approaches-2 of sqrt(8+x^2)

x \to - 2 lim (8 + x^{2})

sum from n=1 to infinity of (-1/2)^n

n = 1 \sum \infty (- \frac{1}{2})^{n}

y^{''}-y^'-2y=8,y(0)=0,y^'(0)=5

y^{^{''}} - y^{^{'}} - 2 y = 8, y (0) = 0, y^{^{'}} (0) = 5

Frequently Asked Questions (FAQ)

What is the derivative of 1/(2x+9) ?
The derivative of 1/(2x+9) is -2/((2x+9)^2)
What is the first derivative of 1/(2x+9) ?
The first derivative of 1/(2x+9) is -2/((2x+9)^2)