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

Lösung

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

4 x^{3} + y x^{y - 1}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{\partial}{\partial x} (x^{y}) = y x^{y - 1}

= 4 x^{3} + 0 + y x^{y - 1}

Vereinfache

= 4 x^{3} + y x^{y - 1}

h \to 0 lim (3 x^{2} - 2 x h + 5 h)

t an g e n t 2 e^{x} cos (x) (0.2)

\int 11 - x^{2} d x

\frac{\partial}{\partial x} (3 cos (x))

d er i v a t i v e f (t) = 4 sec (9) (π t - 2)