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Popular >

derivative of (5x/(7+x))

Solution

\frac{d}{d x} (\frac{5 x}{7 + x})

Solution

\frac{35}{( 7 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5 x}{7 + x})

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{x}{7 + x})

Apply the Quotient Rule:

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

= 5 \cdot \frac{\frac{d x}{d x} ( 7 + x ) - \frac{d}{d x} ( 7 + x ) x}{( 7 + x ) ^{2}}

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

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

= 5 \cdot \frac{1 \cdot ( 7 + x ) - 1 \cdot x}{( 7 + x ) ^{2}}

Simplify

5 \cdot \frac{1 \cdot ( 7 + x ) - 1 \cdot x}{( 7 + x ) ^{2}} : \frac{35}{( 7 + x ) ^{2}}

= \frac{35}{( 7 + x ) ^{2}}

Popular Examples

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(\partial)/(\partial y)(4x^3y^3-3)

\frac{\partial}{\partial y} (4 x^{3} y^{3} - 3)

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\int_{- 1}^{1} x^{2} x^{3} + 1 d x

integral of (x^2+3x)/(sqrt(x+4))

\int \frac{x ^{2} + 3 x}{x + 4} d x

Frequently Asked Questions (FAQ)

What is the derivative of (5x/(7+x)) ?
The derivative of (5x/(7+x)) is (35)/((7+x)^2)
What is the first derivative of (5x/(7+x)) ?
The first derivative of (5x/(7+x)) is (35)/((7+x)^2)