(\partial)/(\partial x)(xln(z^5+x^4))

Lösung

\frac{\partial}{\partial x} (x ln (z^{5} + x^{4}))

ln (z^{5} + x^{4}) + \frac{4 x ^{4}}{z ^{5} + x ^{4}}

Schritte zur Lösung

\frac{\partial}{\partial x} (x ln (z^{5} + x^{4}))

Behandle

z

als Konstante

Wende die Produktregel an:

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

f = x, g = ln (z^{5} + x^{4})

= \frac{\partial}{\partial x} (x) ln (z^{5} + x^{4}) + \frac{\partial}{\partial x} (ln (z^{5} + x^{4})) x

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (ln (z^{5} + x^{4})) = \frac{4 x ^{3}}{z ^{5} + x ^{4}}

= 1 \cdot ln (z^{5} + x^{4}) + \frac{4 x ^{3}}{z ^{5} + x ^{4}} x

Vereinfache

1 \cdot ln (z^{5} + x^{4}) + \frac{4 x ^{3}}{z ^{5} + x ^{4}} x : ln (z^{5} + x^{4}) + \frac{4 x ^{4}}{z ^{5} + x ^{4}}

= ln (z^{5} + x^{4}) + \frac{4 x ^{4}}{z ^{5} + x ^{4}}

\frac{\partial}{\partial x} (7 x y^{2} + 1)

x \to 0 lim ((1 + 5 x)^{\frac{3}{x}})

d er i v a t i v e \frac{( x ^{4} + 2 )}{ln ( x )}

\frac{\partial}{\partial x} (e^{- x y})

n = 0 \sum \infty n^{2} x^{n}