(\partial)/(\partial x)(x^5+4z^2e^{y-x})

Lösung

\frac{\partial}{\partial x} (x^{5} + 4 z^{2} e^{y - x})

5 x^{4} - 4 z^{2} e^{y - x}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{5} + 4 z^{2} e^{y - x})

Behandle

z, y

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{5}) + \frac{\partial}{\partial x} (4 z^{2} e^{y - x})

\frac{\partial}{\partial x} (x^{5}) = 5 x^{4}

\frac{\partial}{\partial x} (4 z^{2} e^{y - x}) = - 4 z^{2} e^{y - x}

= 5 x^{4} - 4 z^{2} e^{y - x}

a re a x^{4}, x

\frac{\partial}{\partial y} (ln (y))

in v erse l a pl a ce \frac{\frac{E}{L}}{( s ^{2} + \frac{1}{C L} )}

d er i v a t i v e y = x^{π}

t an g e n t f (x) = \frac{x}{( 7 x - 6 ) ^{6}}, at x = 1