What is derivative of w(z)=3z^7-7z^3+21z^2 ?

The answer to derivative of w(z)=3z^7-7z^3+21z^2 is (dz)/(dw)=-z/(w-21z^6+21z^2-42z)

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derivative of w(z)=3z^7-7z^3+21z^2

derivative of

w = 3 z^{7} - 7 z^{3} + 21 z^{2}

\frac{d z}{d w} = - \frac{z}{w - 21 z ^{6} + 21 z ^{2} - 42 z}

Solution steps

w z = 3 z^{7} - 7 z^{3} + 21 z^{2}

Treat

z

z (w)

Differentiate both sides:

z + w \frac{d z}{d w} = 21 z^{6} \frac{d z}{d w} - 21 z^{2} \frac{d z}{d w} + 42 z \frac{d z}{d w}

Isolate

\frac{d z}{d w} : \frac{d z}{d w} = - \frac{z}{w - 21 z ^{6} + 21 z ^{2} - 42 z}

\frac{d z}{d w} = - \frac{z}{w - 21 z ^{6} + 21 z ^{2} - 42 z}

\int \frac{1 - 2 x}{1 - 4 x ^{2}} d x

\frac{\partial}{\partial y} (e^{2 y} - y cos (x y))

\int 7 e^{- 0.1 x} d x

\int sin^{2} (x) d x

\frac{d}{d x} (7 x^{2} cos (x) cot (x))

What is derivative of w(z)=3z^7-7z^3+21z^2 ?
The answer to derivative of w(z)=3z^7-7z^3+21z^2 is (dz)/(dw)=-z/(w-21z^6+21z^2-42z)