What is the derivative of e^p(p+psqrt(p)) ?

The derivative of e^p(p+psqrt(p)) is e^p(p+p^{3/2})+(1+(3sqrt(p))/2)e^p

What is the first derivative of e^p(p+psqrt(p)) ?

The first derivative of e^p(p+psqrt(p)) is e^p(p+p^{3/2})+(1+(3sqrt(p))/2)e^p

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derivative of

e^{p} (p + p p)

e^{p} (p + p^{\frac{3}{2}}) + (1 + \frac{3 p}{2}) e^{p}

Solution steps

\frac{d}{d p} (e^{p} (p + p p))

Simplify

e^{p} (p + p p) : e^{p} (p + p^{\frac{3}{2}})

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{p}, g = p + p^{\frac{3}{2}}

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

\frac{d}{d p} (e^{p}) = e^{p}

\frac{d}{d p} (p + p^{\frac{3}{2}}) = 1 + \frac{3 p}{2}

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

What is the derivative of e^p(p+psqrt(p)) ?
The derivative of e^p(p+psqrt(p)) is e^p(p+p^{3/2})+(1+(3sqrt(p))/2)e^p
What is the first derivative of e^p(p+psqrt(p)) ?
The first derivative of e^p(p+psqrt(p)) is e^p(p+p^{3/2})+(1+(3sqrt(p))/2)e^p