Question

differentiate: y=e^p(p+psqrt(p)) ??

Answer 1

simplify this to \[y = e^(p^2 + p^{1/2}.p^{2}) = e^(p^2 + p^(\frac{5}{2}))\]
Now can you solve this?

Answer 2

\(y=e^p(p+p \sqrt p)\)

\(\dfrac{dy}{dp}=e^p \dfrac{d}{dp}(p+p \sqrt p) + (p+p \sqrt p) \dfrac{d}{dp}e^p\)

\(\dfrac{dy}{dp}=e^p \dfrac{d}{dp}(p+p^{\frac{3}{2}}) + (p+p^{\frac{3}{2}}) e^p\)

\(\dfrac{dy}{dp}=e^p (1+\dfrac{3}{2}p^{\frac{1}{2}}) + (p+p^{\frac{3}{2}}) e^p\)

\(\dfrac{dy}{dp}=e^p (1+\dfrac{3}{2}p^{\frac{1}{2}} +p+p^{\frac{3}{2}})\)

Answer 3

chain rule