derivative of 4e^{3x^2}sin(cos(2x))

Lösung

\frac{d}{d x} (4 e^{3 x^{2}} sin (cos (2 x)))

4 (6 e^{3 x^{2}} x sin (cos (2 x)) - 2 e^{3 x^{2}} cos (cos (2 x)) sin (2 x))

Schritte zur Lösung

\frac{d}{d x} (4 e^{3 x^{2}} sin (cos (2 x)))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (e^{3 x^{2}} sin (cos (2 x)))

Wende die Produktregel an:

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

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

= 4 (\frac{d}{d x} (e^{3 x^{2}}) sin (cos (2 x)) + \frac{d}{d x} (sin (cos (2 x))) e^{3 x^{2}})

\frac{d}{d x} (e^{3 x^{2}}) = e^{3 x^{2}} \cdot 6 x

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

= 4 (e^{3 x^{2}} \cdot 6 x sin (cos (2 x)) + (- 2 cos (cos (2 x)) sin (2 x)) e^{3 x^{2}})

Vereinfache

= 4 (6 e^{3 x^{2}} x sin (cos (2 x)) - 2 e^{3 x^{2}} cos (cos (2 x)) sin (2 x))

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

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

\frac{d}{d x} (7^{x} + 7 cos (\frac{7 x}{2}))

x^{2} y^{^{''}} - x y^{^{'}} + y = 0

\int_{1}^{e^{5}} \frac{1}{x ( 1 + ln ( x ) )} d x