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

The derivative of (a^2+x^2/(a^2-x^2)) is (4a^2x)/((a^2-x^2)^2)

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

The first derivative of (a^2+x^2/(a^2-x^2)) is (4a^2x)/((a^2-x^2)^2)

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

\frac{4 a ^{2} x}{( a ^{2} - x ^{2} ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 x ( a ^{2} - x ^{2} ) - ( - 2 x ) ( a ^{2} + x ^{2} )}{( a ^{2} - x ^{2} ) ^{2}} : \frac{4 a ^{2} x}{( a ^{2} - x ^{2} ) ^{2}}

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

\int u^{3} d u

\int (\frac{( ln ( x ^{2} ) )}{x}) d x

\frac{2 x - 1}{4 x + 8}

\int \frac{ln ( x ^{4} )}{x} d x

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