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Popular >

derivative of 6ze^z+3e^zz^2

Solution

derivative of

6 z e^{z} + 3 e^{z} z^{2}

Solution

3 e^{z} z^{2} + 12 e^{z} z + 6 e^{z}

Solution steps

\frac{d}{d z} (6 z e^{z} + 3 e^{z} z^{2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d z} (6 z e^{z}) + \frac{d}{d z} (3 e^{z} z^{2})

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

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

= 6 (e^{z} + e^{z} z) + 3 (e^{z} z^{2} + 2 z e^{z})

Simplify

6 (e^{z} + e^{z} z) + 3 (e^{z} z^{2} + 2 z e^{z}) : 3 e^{z} z^{2} + 12 e^{z} z + 6 e^{z}

= 3 e^{z} z^{2} + 12 e^{z} z + 6 e^{z}

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Frequently Asked Questions (FAQ)

What is the derivative of 6ze^z+3e^zz^2 ?
The derivative of 6ze^z+3e^zz^2 is 3e^zz^2+12e^zz+6e^z
What is the first derivative of 6ze^z+3e^zz^2 ?
The first derivative of 6ze^z+3e^zz^2 is 3e^zz^2+12e^zz+6e^z