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Popular >

derivative of (x^2)/(7+6x)

Solution

derivative of

\frac{x ^{2}}{7 + 6 x}

Solution

\frac{14 x + 6 x ^{2}}{( 7 + 6 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{7 + 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} ) ( 7 + 6 x ) - \frac{d}{d x} ( 7 + 6 x ) x ^{2}}{( 7 + 6 x ) ^{2}}

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

\frac{d}{d x} (7 + 6 x) = 6

= \frac{2 x ( 7 + 6 x ) - 6 x ^{2}}{( 7 + 6 x ) ^{2}}

Expand

2 x (7 + 6 x) - 6 x^{2} : 14 x + 6 x^{2}

= \frac{14 x + 6 x ^{2}}{( 7 + 6 x ) ^{2}}

Popular Examples

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integral of (sec^2(1/x))/(x^2)

\int \frac{sec ^{2} ( \frac{1}{x} )}{x ^{2}} d x

integral of (cot^5(β))/(sqrt(sin(β)))

\int \frac{cot ^{5} ( β )}{sin ( β )} d β

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\int \frac{x}{( 8 - x ^{2} ) ^{2}} d x

5(dy)/(dt)+y=5t

5 \frac{d y}{d t} + y = 5 t

Frequently Asked Questions (FAQ)

What is the derivative of (x^2)/(7+6x) ?
The derivative of (x^2)/(7+6x) is (14x+6x^2)/((7+6x)^2)
What is the first derivative of (x^2)/(7+6x) ?
The first derivative of (x^2)/(7+6x) is (14x+6x^2)/((7+6x)^2)