derivative of e^{3x}sin(x^2)

Lösung

\frac{d}{d x} (e^{3 x} sin (x^{2}))

e^{3 x} \cdot 3 sin (x^{2}) + cos (x^{2}) \cdot 2 x e^{3 x}

Schritte zur Lösung

\frac{d}{d x} (e^{3 x} sin (x^{2}))

Wende die Produktregel an:

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

f = e^{3 x}, g = sin (x^{2})

= \frac{d}{d x} (e^{3 x}) sin (x^{2}) + \frac{d}{d x} (sin (x^{2})) e^{3 x}

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

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

= e^{3 x} \cdot 3 sin (x^{2}) + cos (x^{2}) \cdot 2 x e^{3 x}

a re a 7 x^{2}, x^{2} + 3

x \to 3 lim (\frac{x ^{2} - 9}{3 - x})

y^{^{''}} - 8 y^{^{'}} + 16 y = 0

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

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