What is the derivative of (150x/(x+8)) ?

The derivative of (150x/(x+8)) is (1200)/((x+8)^2)

What is the first derivative of (150x/(x+8)) ?

The first derivative of (150x/(x+8)) is (1200)/((x+8)^2)

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\frac{d}{d x} (\frac{150 x}{x + 8})

\frac{1200}{( x + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{150 x}{x + 8})

Take the constant out:

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

= 150 \frac{d}{d x} (\frac{x}{x + 8})

Apply the Quotient Rule:

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

= 150 \cdot \frac{\frac{d x}{d x} ( x + 8 ) - \frac{d}{d x} ( x + 8 ) x}{( x + 8 ) ^{2}}

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

\frac{d}{d x} (x + 8) = 1

= 150 \cdot \frac{1 \cdot ( x + 8 ) - 1 \cdot x}{( x + 8 ) ^{2}}

Simplify

150 \cdot \frac{1 \cdot ( x + 8 ) - 1 \cdot x}{( x + 8 ) ^{2}} : \frac{1200}{( x + 8 ) ^{2}}

= \frac{1200}{( x + 8 ) ^{2}}

f (x) = (ln (x))^{2}

f (x) = - tan^{2} (x)

y^{^{''}} - 4 y = e^{2 t}

3 x^{2} ln (7 x)

x y^{^{'}} + 2 y = x + 2

What is the derivative of (150x/(x+8)) ?
The derivative of (150x/(x+8)) is (1200)/((x+8)^2)
What is the first derivative of (150x/(x+8)) ?
The first derivative of (150x/(x+8)) is (1200)/((x+8)^2)