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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

3 x ln (1 + x)

\int x^{\frac{1}{3}} + (2 x)^{\frac{1}{3}} d x

y^{^{'}} - 2 y = e^{2 t}

y = 13 - x^{2}, y = x^{2} - 5

\frac{d y}{d x} - sin (x) y = 2 sin (x)

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