What is derivative of w(z)=(3z)/(1+2z) ?

The answer to derivative of w(z)=(3z)/(1+2z) is (dz)/(dw)=(-z-4z^2-4z^3)/(w(1+2z)^2-3)

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derivative of w(z)=(3z)/(1+2z)

derivative of

w = \frac{3 z}{1 + 2 z}

\frac{d z}{d w} = \frac{- z - 4 z ^{2} - 4 z ^{3}}{w ( 1 + 2 z ) ^{2} - 3}

Solution steps

w z = \frac{3 z}{1 + 2 z}

Treat

z

z (w)

Differentiate both sides:

z + w \frac{d z}{d w} = \frac{3 \frac{d z}{d w}}{( 1 + 2 z ) ^{2}}

Isolate

\frac{d z}{d w} : \frac{d z}{d w} = \frac{- z - 4 z ^{2} - 4 z ^{3}}{w ( 1 + 2 z ) ^{2} - 3}

\frac{d z}{d w} = \frac{- z - 4 z ^{2} - 4 z ^{3}}{w ( 1 + 2 z ) ^{2} - 3}

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What is derivative of w(z)=(3z)/(1+2z) ?
The answer to derivative of w(z)=(3z)/(1+2z) is (dz)/(dw)=(-z-4z^2-4z^3)/(w(1+2z)^2-3)