derivative of x,x^2,x^3

Lösung

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

(,, (1 \cdot x^{2} x^{3} + 5 x^{4} x))

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = x^{2} x^{3}

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

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{2} x^{3}) = 5 x^{4}

= (,, (1 \cdot x^{2} x^{3} + 5 x^{4} x))

\frac{d}{d x} (\frac{1}{a ^{2} + x ^{2}})

\frac{d}{d x} (sin^{2} (\frac{x}{x + 1}))

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

x \to 7 lim (\frac{x - 7}{3 x ^{2} - 21 x})

\frac{\partial}{\partial x} (ln (x) + z ln (y))