What is the derivative of (2000x/(4x+75)) ?

The derivative of (2000x/(4x+75)) is (150000)/((4x+75)^2)

What is the first derivative of (2000x/(4x+75)) ?

The first derivative of (2000x/(4x+75)) is (150000)/((4x+75)^2)

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\frac{d}{d x} (\frac{2000 x}{4 x + 75})

\frac{150000}{( 4 x + 75 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2000 x}{4 x + 75})

Take the constant out:

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

= 2000 \frac{d}{d x} (\frac{x}{4 x + 75})

Apply the Quotient Rule:

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

= 2000 \cdot \frac{\frac{d x}{d x} ( 4 x + 75 ) - \frac{d}{d x} ( 4 x + 75 ) x}{( 4 x + 75 ) ^{2}}

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

\frac{d}{d x} (4 x + 75) = 4

= 2000 \cdot \frac{1 \cdot ( 4 x + 75 ) - 4 x}{( 4 x + 75 ) ^{2}}

Simplify

2000 \cdot \frac{1 \cdot ( 4 x + 75 ) - 4 x}{( 4 x + 75 ) ^{2}} : \frac{150000}{( 4 x + 75 ) ^{2}}

= \frac{150000}{( 4 x + 75 ) ^{2}}

What is the derivative of (2000x/(4x+75)) ?
The derivative of (2000x/(4x+75)) is (150000)/((4x+75)^2)
What is the first derivative of (2000x/(4x+75)) ?
The first derivative of (2000x/(4x+75)) is (150000)/((4x+75)^2)