What is the d/(dz)((az^2)/(a^2+z^2)) ?

The d/(dz)((az^2)/(a^2+z^2)) is (2a^3z)/((a^2+z^2)^2)

What is the first d/(dz)((az^2)/(a^2+z^2)) ?

The first d/(dz)((az^2)/(a^2+z^2)) is (2a^3z)/((a^2+z^2)^2)

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

\frac{2 a ^{3} z}{( a ^{2} + z ^{2} ) ^{2}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

a \frac{2 z ( a ^{2} + z ^{2} ) - 2 z z ^{2}}{( a ^{2} + z ^{2} ) ^{2}} : \frac{2 a ^{3} z}{( a ^{2} + z ^{2} ) ^{2}}

= \frac{2 a ^{3} z}{( a ^{2} + z ^{2} ) ^{2}}

\int x^{3} x^{2} - 7 d x

\frac{\partial}{\partial t} (r \cdot sin (t))

\int a (x) d x

\frac{\partial}{\partial z} (3.5 yz cos (x yz))

\int \frac{1}{x ^{3} 9 x ^{2} - 1} d x

What is the d/(dz)((az^2)/(a^2+z^2)) ?
The d/(dz)((az^2)/(a^2+z^2)) is (2a^3z)/((a^2+z^2)^2)
What is the first d/(dz)((az^2)/(a^2+z^2)) ?
The first d/(dz)((az^2)/(a^2+z^2)) is (2a^3z)/((a^2+z^2)^2)