What is the derivative of (250x/(x+3)) ?

The derivative of (250x/(x+3)) is (750)/((x+3)^2)

What is the first derivative of (250x/(x+3)) ?

The first derivative of (250x/(x+3)) is (750)/((x+3)^2)

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\frac{d}{d x} (\frac{250 x}{x + 3})

\frac{750}{( x + 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{250 x}{x + 3})

Take the constant out:

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

= 250 \frac{d}{d x} (\frac{x}{x + 3})

Apply the Quotient Rule:

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

= 250 \cdot \frac{\frac{d x}{d x} ( x + 3 ) - \frac{d}{d x} ( x + 3 ) x}{( x + 3 ) ^{2}}

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

\frac{d}{d x} (x + 3) = 1

= 250 \cdot \frac{1 \cdot ( x + 3 ) - 1 \cdot x}{( x + 3 ) ^{2}}

Simplify

250 \cdot \frac{1 \cdot ( x + 3 ) - 1 \cdot x}{( x + 3 ) ^{2}} : \frac{750}{( x + 3 ) ^{2}}

= \frac{750}{( x + 3 ) ^{2}}

x \to 0 - lim (\frac{1}{1 + e \frac{1}{x}})

2 + 5 x

\frac{\partial}{\partial x} (\frac{q ( x , r , s , t ) x + r}{s x + t})

\frac{d}{d x} (sinh (cosh (x)))

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

What is the derivative of (250x/(x+3)) ?
The derivative of (250x/(x+3)) is (750)/((x+3)^2)
What is the first derivative of (250x/(x+3)) ?
The first derivative of (250x/(x+3)) is (750)/((x+3)^2)