(\partial)/(\partial x)(sqrt(5+2x+3xy^2))

Lösung

\frac{\partial}{\partial x} (5 + 2 x + 3 x y^{2})

\frac{3 y ^{2} + 2}{2 5 + 2 x + 3 x y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (5 + 2 x + 3 x y^{2})

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{2 5 + 2 x + 3 x y ^{2}} \frac{\partial}{\partial x} (5 + 2 x + 3 x y^{2})

= \frac{1}{2 5 + 2 x + 3 x y ^{2}} \frac{\partial}{\partial x} (5 + 2 x + 3 x y^{2})

\frac{\partial}{\partial x} (5 + 2 x + 3 x y^{2}) = 3 y^{2} + 2

= \frac{1}{2 5 + 2 x + 3 x y ^{2}} (3 y^{2} + 2)

Vereinfache

\frac{1}{2 5 + 2 x + 3 x y ^{2}} (3 y^{2} + 2) : \frac{3 y ^{2} + 2}{2 5 + 2 x + 3 x y ^{2}}

= \frac{3 y ^{2} + 2}{2 5 + 2 x + 3 x y ^{2}}

\int cos (16 x) cos (7 x) d x

\frac{d ^{2}}{d x ^{2}} (x^{r})

in v erse l a pl a ce \frac{1}{s ^{2} + 5}

n = 0 \sum \infty (n + 1) (\frac{1}{2})^{n}

t a y l or \frac{1}{1 - x ^{5}}