Question

Find the derivative

h(y) = ay* e^(by)
find dh/dy

Answer 1

Use the product rule
\[h'=aybe^{by}+ae^{by}\]

Answer 2

\[\frac{ dh }{ dy } = ay ^{by}\]

apply product rule.

Answer 3

\[ay*e ^{by} = ay'(e ^{by}) + ay(e ^{by})'\]

Answer 4

But in this case y'=1

Answer 5

\[\frac{ dh }{dy }aye ^{by}+ ay \frac{ dh }{ dy }e ^{by} = ae ^{by} + abye ^{by}\]

\[\frac{ dh }{ dy } = ae ^{by}(1+by)\]

@benitob