derivative of x^2*sin(x^3)

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

cos (x^{3}) \cdot 3 x^{2} x^{2} = 3 x^{4} cos (x^{3})

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

\frac{d}{d x} (\frac{8 e ^{6 x}}{5 x + 2})

\int \frac{1}{2} + \frac{x ^{4}}{4} + \frac{1}{4 x ^{4}} d x

y^{^{''}} + 4 y^{^{'}} + 4 y = 12 t + 16

\int_{0}^{10} 1 + 16 x^{2} d x

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