(\partial)/(\partial y)(1+x^3+y^4)

Lösung

\frac{\partial}{\partial y} (1 + x^{3} + y^{4})

4 y^{3}

Schritte zur Lösung

\frac{\partial}{\partial y} (1 + x^{3} + y^{4})

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (1) + \frac{\partial}{\partial y} (x^{3}) + \frac{\partial}{\partial y} (y^{4})

\frac{\partial}{\partial y} (1) = 0

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

\frac{\partial}{\partial y} (y^{4}) = 4 y^{3}

= 0 + 0 + 4 y^{3}

Vereinfache

= 4 y^{3}

\frac{d x}{d t} = 0.25 - \frac{1}{20} x, x (0) = 0.5

y^{^{''}} + 25 y = 3 sec^{3} (5)

s im pl i f y \frac{x}{x ^{2} + y ^{2}}

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

\frac{d}{d x} (2 x^{- 3})