(\partial)/(\partial x)(yln(x^4+y^3+2)-3)

Lösung

\frac{\partial}{\partial x} (y ln (x^{4} + y^{3} + 2) - 3)

\frac{4 y x ^{3}}{y ^{3} + x ^{4} + 2}

Schritte zur Lösung

\frac{\partial}{\partial x} (y ln (x^{4} + y^{3} + 2) - 3)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (y ln (x^{4} + y^{3} + 2)) - \frac{\partial}{\partial x} (3)

\frac{\partial}{\partial x} (y ln (x^{4} + y^{3} + 2)) = \frac{4 y x ^{3}}{x ^{4} + y ^{3} + 2}

\frac{\partial}{\partial x} (3) = 0

= \frac{4 y x ^{3}}{x ^{4} + y ^{3} + 2} - 0

Vereinfache

= \frac{4 y x ^{3}}{y ^{3} + x ^{4} + 2}

\frac{d ^{2}}{d x ^{2}} (sin (b x) - 2 cos (b x))

\int \frac{1}{b x} d x

h \to 0 lim ((1 + h)^{\frac{1}{h}})

n = 1 \sum \infty n^{- \frac{1}{2}}

d er i v a t i v e y = \frac{x ^{4}}{1 - x ^{3}}