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Popular >

derivative of (2x/(x+9))

Solution

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

Solution

\frac{18}{( x + 9 ) ^{2}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

Simplify

2 \cdot \frac{1 \cdot ( x + 9 ) - 1 \cdot x}{( x + 9 ) ^{2}} : \frac{18}{( x + 9 ) ^{2}}

= \frac{18}{( x + 9 ) ^{2}}

Popular Examples

(\partial)/(\partial x)(8-x^2+xy-4y^2)

\frac{\partial}{\partial x} (8 - x^{2} + x y - 4 y^{2})

integral of (ln(x))/(e^x)

\int \frac{ln ( x )}{e ^{x}} d x

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n = 1 \sum \infty \frac{x ^{n}}{8 ^{n}}

derivative of (x^2+1)^{1/2}derivative of

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Frequently Asked Questions (FAQ)

What is the derivative of (2x/(x+9)) ?
The derivative of (2x/(x+9)) is (18)/((x+9)^2)
What is the first derivative of (2x/(x+9)) ?
The first derivative of (2x/(x+9)) is (18)/((x+9)^2)