What is the derivative of (0.14x/(0.15+x)) ?

The derivative of (0.14x/(0.15+x)) is (0.021)/((0.15+x)^2)

What is the first derivative of (0.14x/(0.15+x)) ?

The first derivative of (0.14x/(0.15+x)) is (0.021)/((0.15+x)^2)

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\frac{d}{d x} (\frac{0.14 x}{0.15 + x})

\frac{0.021}{( 0.15 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{0.14 x}{0.15 + x})

Take the constant out:

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

= 0.14 \frac{d}{d x} (\frac{x}{0.15 + x})

Apply the Quotient Rule:

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

= 0.14 \cdot \frac{\frac{d x}{d x} ( 0.15 + x ) - \frac{d}{d x} ( 0.15 + x ) x}{( 0.15 + x ) ^{2}}

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

\frac{d}{d x} (0.15 + x) = 1

= 0.14 \cdot \frac{1 \cdot ( 0.15 + x ) - 1 \cdot x}{( 0.15 + x ) ^{2}}

Simplify

0.14 \cdot \frac{1 \cdot ( 0.15 + x ) - 1 \cdot x}{( 0.15 + x ) ^{2}} : \frac{0.021}{( 0.15 + x ) ^{2}}

= \frac{0.021}{( 0.15 + x ) ^{2}}

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What is the derivative of (0.14x/(0.15+x)) ?
The derivative of (0.14x/(0.15+x)) is (0.021)/((0.15+x)^2)
What is the first derivative of (0.14x/(0.15+x)) ?
The first derivative of (0.14x/(0.15+x)) is (0.021)/((0.15+x)^2)