derivative f(x)=x^2sin(4x^2)

Lösung

ableitung von

f (x) = x^{2} sin (4 x^{2})

2 x sin (4 x^{2}) + 8 x^{3} cos (4 x^{2})

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2}, g = sin (4 x^{2})

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

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

\frac{d}{d x} (sin (4 x^{2})) = cos (4 x^{2}) \cdot 8 x

= 2 x sin (4 x^{2}) + cos (4 x^{2}) \cdot 8 x x^{2}

cos (4 x^{2}) \cdot 8 x x^{2} = 8 x^{3} cos (4 x^{2})

= 2 x sin (4 x^{2}) + 8 x^{3} cos (4 x^{2})

\frac{\partial}{\partial x} (2 z)

d er i v a t i v e (\frac{4 - 80 y}{y}) (y - 48)

\frac{\partial}{\partial x} (f (x))

\int \frac{1}{x ^{2} - 4 x + 5} d x

\int 8 x - x^{2} d x