(\partial)/(\partial y)(x^5+2^y+x^y)

Lösung

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

x^{y} ln (x) + ln (2) \cdot 2^{y}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial y} (x^{5}) = 0

\frac{\partial}{\partial y} (2^{y}) = 2^{y} ln (2)

\frac{\partial}{\partial y} (x^{y}) = x^{y} ln (x)

= 0 + 2^{y} ln (2) + x^{y} ln (x)

Vereinfache

= x^{y} ln (x) + ln (2) \cdot 2^{y}

x \to 2 - lim (x + 2)

y^{^{''''}} + 20 y^{^{''}} + 100 y = 0

y^{^{'}} = e^{5 x + 3 y}

f (t) = cos^{3} (t)

y^{^{''}} - y^{^{'}} - 2 y = e^{3 x} sin (2 x)