derivative of 3x^2cos(x^3)

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (cos (x^{3})) = - sin (x^{3}) \cdot 3 x^{2}

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

Vereinfache

3 (2 x cos (x^{3}) + (- sin (x^{3}) \cdot 3 x^{2}) x^{2}) : 3 (2 x cos (x^{3}) - 3 x^{4} sin (x^{3}))

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

\frac{d y}{d t} + 3 y = cos (2 t)

\int (4 x^{2} + 1)^{4} + (4 x^{2} + 1)^{3} d x

\int sin (x) sin (y) d y

\int \frac{1}{7 x ^{4}} d x

\int e^{x} \cdot sin (x - π) d x