derivative of sin(x+x^2e^y+5)

Lösung

\frac{d}{d x} (sin (x) + x^{2} e^{y} + 5)

e^{y} x^{2} \frac{d y}{d x} + 2 e^{y} x + cos (x)

Schritte zur Lösung

\frac{d}{d x} (sin (x) + x^{2} e^{y} + 5)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (sin (x)) + \frac{d}{d x} (x^{2} e^{y}) + \frac{d}{d x} (5)

\frac{d}{d x} (sin (x)) = cos (x)

\frac{d}{d x} (x^{2} e^{y}) = 2 x e^{y} + e^{y} \frac{d y}{d x} x^{2}

\frac{d}{d x} (5) = 0

= cos (x) + 2 x e^{y} + e^{y} \frac{d y}{d x} x^{2} + 0

Vereinfache

= e^{y} x^{2} \frac{d y}{d x} + 2 e^{y} x + cos (x)

\int x cosh (x^{2}) d x

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

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

2 (12) (5) + 2 (5) \frac{d y}{d t} = 0

\int 11 cot^{4} (x) d x