What is the derivative of (x^2/(5x+2)) ?

The derivative of (x^2/(5x+2)) is (5x^2+4x)/((5x+2)^2)

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

The first derivative of (x^2/(5x+2)) is (5x^2+4x)/((5x+2)^2)

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\frac{d}{d x} (\frac{x ^{2}}{5 x + 2})

\frac{5 x ^{2} + 4 x}{( 5 x + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{5 x + 2})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (5 x + 2) = 5

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

Expand

2 x (5 x + 2) - 5 x^{2} : 5 x^{2} + 4 x

= \frac{5 x ^{2} + 4 x}{( 5 x + 2 ) ^{2}}

What is the derivative of (x^2/(5x+2)) ?
The derivative of (x^2/(5x+2)) is (5x^2+4x)/((5x+2)^2)
What is the first derivative of (x^2/(5x+2)) ?
The first derivative of (x^2/(5x+2)) is (5x^2+4x)/((5x+2)^2)