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Popular >

derivative of x/(x+20)

Solution

\frac{d}{d x} (\frac{x}{x + 20})

Solution

\frac{20}{( x + 20 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x + 20})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x + 20 ) - \frac{d}{d x} ( x + 20 ) x}{( x + 20 ) ^{2}}

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

\frac{d}{d x} (x + 20) = 1

= \frac{1 \cdot ( x + 20 ) - 1 \cdot x}{( x + 20 ) ^{2}}

1 \cdot (x + 20) - 1 \cdot x = 20

= \frac{20}{( x + 20 ) ^{2}}

Popular Examples

integral of (2x)/(x+2)

\int \frac{2 x}{x + 2} d x

(dy)/(dx)=0.0225y+0.0003y^2

\frac{d y}{d x} = 0.0225 y + 0.0003 y^{2}

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

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

(\partial)/(\partial x)(x^2y+3xy+y^2)

\frac{\partial}{\partial x} (x^{2} y + 3 x y + y^{2})

limit as x approaches infinity of (((2x-3))/((2x+5)))^{2x+1}

x \to \infty lim ((\frac{( 2 x - 3 )}{( 2 x + 5 )})^{2 x + 1})

Frequently Asked Questions (FAQ)

What is the derivative of x/(x+20) ?
The derivative of x/(x+20) is (20)/((x+20)^2)
What is the first derivative of x/(x+20) ?
The first derivative of x/(x+20) is (20)/((x+20)^2)