(\partial)/(\partial x)(3-(e^y)/(e^{x+1)})

Lösung

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

e^{y - x - 1}

Schritte zur Lösung

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

Vereinfache

3 - \frac{e ^{y}}{e ^{x + 1}} : 3 - e^{y - x - 1}

= \frac{\partial}{\partial x} (3 - e^{y - x - 1})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (3) - \frac{\partial}{\partial x} (e^{y - x - 1})

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

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

= 0 - (- e^{y - x - 1})

Vereinfache

= e^{y - x - 1}

d er i v a t i v e f (x) = 7 x^{6}

t an g e n t f (x) = 2 x^{2} + 3 x - 2, at x = 0

\int (3 x^{2} + 2 x - 1) d x

x \to 1 + lim (x^{3})

\int \frac{1 + x ^{2}}{- 9 x} d x