derivative of {f}(xsqrt(x))

Lösung

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

x \frac{d}{d x} (f (x)) + \frac{f ( x )}{2 x}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = f (x), g = x

= \frac{d}{d x} (f (x)) x + \frac{d}{d x} (x) f (x)

\frac{d}{d x} (x) = \frac{1}{2 x}

= \frac{d}{d x} (f (x)) x + \frac{1}{2 x} f (x)

\frac{1}{2 x} f (x) = \frac{f ( x )}{2 x}

= x \frac{d}{d x} (f (x)) + \frac{f ( x )}{2 x}

x \to - 3 + lim (\frac{∣ x + 3 ∣}{x + 3})

\int_{- 4}^{0} y + 4 d y

\int \frac{10 x + 2}{( 3 x + 1 ) ( x - 1 )} d x

\int x^{2} + 8 d x

d er i v a t i v e y