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Popular >

derivative of ((x^2))/(5+6x)

Solution

derivative of

\frac{( x ^{2} )}{5 + 6 x}

Solution

\frac{10 x + 6 x ^{2}}{( 5 + 6 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{5 + 6 x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 5 + 6 x ) - \frac{d}{d x} ( 5 + 6 x ) x ^{2}}{( 5 + 6 x ) ^{2}}

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

\frac{d}{d x} (5 + 6 x) = 6

= \frac{2 x ( 5 + 6 x ) - 6 x ^{2}}{( 5 + 6 x ) ^{2}}

Expand

2 x (5 + 6 x) - 6 x^{2} : 10 x + 6 x^{2}

= \frac{10 x + 6 x ^{2}}{( 5 + 6 x ) ^{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of ((x^2))/(5+6x) ?
The derivative of ((x^2))/(5+6x) is (10x+6x^2)/((5+6x)^2)
What is the first derivative of ((x^2))/(5+6x) ?
The first derivative of ((x^2))/(5+6x) is (10x+6x^2)/((5+6x)^2)