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

Lösung

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

2 x sin^{2} (x) + sin (2 x) x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

= 2 x sin^{2} (x) + sin (2 x) x^{2}

t an g e n t f (x) = \frac{36 x}{x ^{2} + 36}, (- 3, - \frac{12}{5})

\frac{d}{d x} ((sin (x) + cos (x)) sec (x) d x)

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

\int t^{2} - cos (2 π) t d t

\int sin^{2} (d) t