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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

= \frac{1 \cdot ( 7 + x ^{2} ) - 2 xx}{( 7 + x ^{2} ) ^{2}}

1 \cdot (7 + x^{2}) - 2 xx = 7 - x^{2}

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

\int (cot (x))^{2} d x

\int x^{2} \cdot e^{x^{3}} d x

\frac{d}{d x} (- \frac{2 x ^{3}}{y})

\int \frac{y}{( y + 2 ) ( 4 y - 1 )} d y

y = 4.5 x^{2} - 3 x + 2

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