What is the derivative of (x^2/(9-x^2)) ?

The derivative of (x^2/(9-x^2)) is (18x)/((9-x^2)^2)

What is the first derivative of (x^2/(9-x^2)) ?

The first derivative of (x^2/(9-x^2)) is (18x)/((9-x^2)^2)

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\frac{d}{d x} (\frac{x ^{2}}{9 - x ^{2}})

\frac{18 x}{( 9 - x ^{2} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{9 - x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 9 - x ^{2} ) - \frac{d}{d x} ( 9 - x ^{2} ) x ^{2}}{( 9 - x ^{2} ) ^{2}}

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

\frac{d}{d x} (9 - x^{2}) = - 2 x

= \frac{2 x ( 9 - x ^{2} ) - ( - 2 x ) x ^{2}}{( 9 - x ^{2} ) ^{2}}

Simplify

\frac{2 x ( 9 - x ^{2} ) - ( - 2 x ) x ^{2}}{( 9 - x ^{2} ) ^{2}} : \frac{18 x}{( 9 - x ^{2} ) ^{2}}

= \frac{18 x}{( 9 - x ^{2} ) ^{2}}

\frac{\partial}{\partial x} (2 y x)

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

f (x) = \frac{( x + 1 ) ( 3 x - 7 )}{3 x + 1}

\int x^{4} 9 + x^{5} d x

\int 11 x^{\frac{4}{7}} + 4 x^{- \frac{6}{7}} d x

What is the derivative of (x^2/(9-x^2)) ?
The derivative of (x^2/(9-x^2)) is (18x)/((9-x^2)^2)
What is the first derivative of (x^2/(9-x^2)) ?
The first derivative of (x^2/(9-x^2)) is (18x)/((9-x^2)^2)