derivative of (x^2ln(x)^4)

Lösung

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

8 x^{7} ln^{4} (x) + 4 x^{7} ln^{3} (x)

Schritte zur Lösung

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

Vereinfache

(x^{2} ln (x))^{4} : x^{8} ln^{4} (x)

= \frac{d}{d x} (x^{8} ln^{4} (x))

Wende die Produktregel an:

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

f = x^{8}, g = ln^{4} (x)

= \frac{d}{d x} (x^{8}) ln^{4} (x) + \frac{d}{d x} (ln^{4} (x)) x^{8}

\frac{d}{d x} (x^{8}) = 8 x^{7}

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

= 8 x^{7} ln^{4} (x) + \frac{4 ln ^{3} ( x )}{x} x^{8}

\frac{4 ln ^{3} ( x )}{x} x^{8} = 4 x^{7} ln^{3} (x)

= 8 x^{7} ln^{4} (x) + 4 x^{7} ln^{3} (x)

d er i v a t i v e y = \frac{1}{3} cos (\frac{6 π x - 1}{2})

\int - e^{x} - \frac{7}{cos ^{2} ( x )} d x

\int \frac{3}{2} e^{\frac{3}{2} x} d x

d er i v a t i v e e^{3} ln (e^{3})

(4 x - 3 y) d x + (2 y - 3 x) d y = 0