What is the derivative of (10x)/((x+7)) ?

The derivative of (10x)/((x+7)) is (70)/((x+7)^2)

What is the first derivative of (10x)/((x+7)) ?

The first derivative of (10x)/((x+7)) is (70)/((x+7)^2)

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derivative of

\frac{10 x}{( x + 7 )}

\frac{70}{( x + 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{10 x}{x + 7})

Take the constant out:

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

= 10 \frac{d}{d x} (\frac{x}{x + 7})

Apply the Quotient Rule:

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

= 10 \cdot \frac{\frac{d x}{d x} ( x + 7 ) - \frac{d}{d x} ( x + 7 ) x}{( x + 7 ) ^{2}}

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

\frac{d}{d x} (x + 7) = 1

= 10 \cdot \frac{1 \cdot ( x + 7 ) - 1 \cdot x}{( x + 7 ) ^{2}}

Simplify

10 \cdot \frac{1 \cdot ( x + 7 ) - 1 \cdot x}{( x + 7 ) ^{2}} : \frac{70}{( x + 7 ) ^{2}}

= \frac{70}{( x + 7 ) ^{2}}

3 - x

\frac{( x + 1 ) ^{2}}{x}

\frac{150}{r ^{2}}

3 \frac{x ^{2}}{x} - \frac{2}{x}

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

What is the derivative of (10x)/((x+7)) ?
The derivative of (10x)/((x+7)) is (70)/((x+7)^2)
What is the first derivative of (10x)/((x+7)) ?
The first derivative of (10x)/((x+7)) is (70)/((x+7)^2)