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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

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

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

\int ln (1 + \frac{1}{x}) d x

x^{2} y^{^{''}} + 17 x y^{^{'}} + 113 y = 0

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

n = 0 \sum \infty \frac{7}{3 ^{n}}

\frac{d}{d x} (cosh (k x))

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