d/(dp)(e^p(p+psqrt(p)))

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Produktregel an:

(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}

x \to - 4 lim (x^{2})

l a pl a ce t r an s f or m 5

\int \frac{5}{t} d t

\int \frac{1}{3 ( x ^{2} + 1 )} d x

t an g e n t y = \frac{3 x}{2 ^{x}}, at x = 2