What is the derivative of (x^2/(7+4x)) ?

The derivative of (x^2/(7+4x)) is (14x+4x^2)/((7+4x)^2)

What is the first derivative of (x^2/(7+4x)) ?

The first derivative of (x^2/(7+4x)) is (14x+4x^2)/((7+4x)^2)

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\frac{d}{d x} (\frac{x ^{2}}{7 + 4 x})

\frac{14 x + 4 x ^{2}}{( 7 + 4 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{7 + 4 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 + 4 x ) - \frac{d}{d x} ( 7 + 4 x ) x ^{2}}{( 7 + 4 x ) ^{2}}

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

\frac{d}{d x} (7 + 4 x) = 4

= \frac{2 x ( 7 + 4 x ) - 4 x ^{2}}{( 7 + 4 x ) ^{2}}

Expand

2 x (7 + 4 x) - 4 x^{2} : 14 x + 4 x^{2}

= \frac{14 x + 4 x ^{2}}{( 7 + 4 x ) ^{2}}

\int \frac{6}{9 - x ^{2}} d x

\int \frac{x ^{4}}{1 - x ^{5}} d x

\int \frac{1}{x - 5} d x

\int \frac{1}{400 - x ^{2}} d x

t (x) v^{''} + v^{'} = 0

What is the derivative of (x^2/(7+4x)) ?
The derivative of (x^2/(7+4x)) is (14x+4x^2)/((7+4x)^2)
What is the first derivative of (x^2/(7+4x)) ?
The first derivative of (x^2/(7+4x)) is (14x+4x^2)/((7+4x)^2)