What is the d/(da)(a/(a^2+b^2)) ?

The d/(da)(a/(a^2+b^2)) is (-a^2+b^2)/((a^2+b^2)^2)

What is the first d/(da)(a/(a^2+b^2)) ?

The first d/(da)(a/(a^2+b^2)) is (-a^2+b^2)/((a^2+b^2)^2)

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\frac{d}{d a} (\frac{a}{a ^{2} + b ^{2}})

\frac{- a ^{2} + b ^{2}}{( a ^{2} + b ^{2} ) ^{2}}

Solution steps

\frac{d}{d a} (\frac{a}{a ^{2} + b ^{2}})

Apply the Quotient Rule:

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

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

\frac{d a}{d a} = 1

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

= \frac{1 \cdot ( a ^{2} + b ^{2} ) - 2 aa}{( a ^{2} + b ^{2} ) ^{2}}

1 \cdot (a^{2} + b^{2}) - 2 aa = - a^{2} + b^{2}

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

\frac{d}{d x} (sin (arctan (x)))

\int x 2^{x^{2}} d x

\int + \frac{x}{x ^{4} + 7} d x

\frac{d}{d x} (\frac{3}{1 - 2 x})

\int_{0}^{\frac{1}{2}} 8 arccos (x) d x

What is the d/(da)(a/(a^2+b^2)) ?
The d/(da)(a/(a^2+b^2)) is (-a^2+b^2)/((a^2+b^2)^2)
What is the first d/(da)(a/(a^2+b^2)) ?
The first d/(da)(a/(a^2+b^2)) is (-a^2+b^2)/((a^2+b^2)^2)