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)

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

\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}}

\int 5 (1 - x)^{4} d x

\int \frac{24}{x ^{3}} d x

x \to 1 lim (\frac{x - 3}{x ^{2} + 4})

\frac{d y}{d x} = x + y, y (0) = 3

\frac{2}{65 + 4 t}

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)