What is derivative of w(z)=6z^2e^z ?

The answer to derivative of w(z)=6z^2e^z is (dz)/(dw)=-z/(w-12e^zz-6e^zz^2)

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derivative of w(z)=6z^2e^z

derivative of

w (z) = 6 z^{2} e^{z}

\frac{d z}{d w} = - \frac{z}{w - 12 e ^{z} z - 6 e ^{z} z ^{2}}

Solution steps

w z = 6 z^{2} e^{z}

Treat

z

z (w)

Differentiate both sides:

z + w \frac{d z}{d w} = 6 (2 z \frac{d z}{d w} e^{z} + e^{z} \frac{d z}{d w} z^{2})

Isolate

\frac{d z}{d w} : \frac{d z}{d w} = - \frac{z}{w - 12 e ^{z} z - 6 e ^{z} z ^{2}}

\frac{d z}{d w} = - \frac{z}{w - 12 e ^{z} z - 6 e ^{z} z ^{2}}

What is derivative of w(z)=6z^2e^z ?
The answer to derivative of w(z)=6z^2e^z is (dz)/(dw)=-z/(w-12e^zz-6e^zz^2)