derivative of sin(e^{x^2}*cos(x))

Lösung

\frac{d}{d x} (sin (e^{x^{2}}) \cdot cos (x))

2 e^{x^{2}} x cos (e^{x^{2}}) cos (x) - sin (x) sin (e^{x^{2}})

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (e^{x^{2}}), g = cos (x)

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

\frac{d}{d x} (sin (e^{x^{2}})) = cos (e^{x^{2}}) e^{x^{2}} \cdot 2 x

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

= cos (e^{x^{2}}) e^{x^{2}} \cdot 2 x cos (x) + (- sin (x)) sin (e^{x^{2}})

Vereinfache

= 2 e^{x^{2}} x cos (e^{x^{2}}) cos (x) - sin (x) sin (e^{x^{2}})

\int \frac{1}{x ^{3} - 3 x ^{2}} d x

\frac{d}{d x} (x^{2} - 3 x + 12)

t an g e n t f (x) = 2 sin (x), at x = \frac{3 π}{4}

y^{^{'}} = sin (5 x), y (0) = 2

(x + 1) \frac{d y}{d x} + (x + 2) y = 8 x e^{- x}