How do you find the first derivative of #f(z) = z^2 e^(2z)#?

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Answer 1 · 2018-04-12T13:34:47

#f'(z)=2ze^(2z)(z+1)#

The Product Rule tells us that if we have a multiplication of functions #(fg),# then

#(fg)'=fg'+gf'#

Here,

#f(z)=z^2e^(2z)#

#f'(z)=z^2d/dze^(2z)+e^(2z)d/dzz^2#

#d/dzz^2=dz#

#d/dze^(2z)=2e^(2z)#

As per the Product Rule and Chain Rule. So,

#f'(z)=2z^2e^(2z)+2ze^(2z)#

We may simplify a bit.

#f'(z)=2ze^(2z)(z+1)#