derivative of sin(4x+7x^4+e^{1-x^2})

Lösung

\frac{d}{d x} (sin (4 x + 7 x^{4}) + e^{1 - x^{2}})

cos (4 x + 7 x^{4}) (4 + 28 x^{3}) - 2 e^{1 - x^{2}} x

Schritte zur Lösung

\frac{d}{d x} (sin (4 x + 7 x^{4}) + e^{1 - x^{2}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (sin (4 x + 7 x^{4})) + \frac{d}{d x} (e^{1 - x^{2}})

\frac{d}{d x} (sin (4 x + 7 x^{4})) = cos (4 x + 7 x^{4}) (4 + 28 x^{3})

\frac{d}{d x} (e^{1 - x^{2}}) = - 2 e^{1 - x^{2}} x

= cos (4 x + 7 x^{4}) (4 + 28 x^{3}) - 2 e^{1 - x^{2}} x

\int \frac{x ^{2} + 24 x - 9}{x ^{3} - 9 x} d x

x \to \frac{π}{2} lim (- cos (x))

d er i v a t i v e y = \frac{6 x ^{2} + 6 x + 2}{x}

d er i v a t i v e 5 cos (x)

\frac{\partial}{\partial x} (x ln (t))