derivative of x^8ln(9x)

Lösung

\frac{d}{d x} (x^{8} ln (9 x))

8 x^{7} ln (9 x) + x^{7}

Schritte zur Lösung

\frac{d}{d x} (x^{8} ln (9 x))

Wende die Produktregel an:

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

f = x^{8}, g = ln (9 x)

= \frac{d}{d x} (x^{8}) ln (9 x) + \frac{d}{d x} (ln (9 x)) x^{8}

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

\frac{d}{d x} (ln (9 x)) = \frac{1}{x}

= 8 x^{7} ln (9 x) + \frac{1}{x} x^{8}

\frac{1}{x} x^{8} = x^{7}

= 8 x^{7} ln (9 x) + x^{7}

y^{^{'}} + 2 y = 3, y (0) = 0

\frac{d}{d x} (4^{s i n^{2} (x) + c o s (3 x)})

\int_{0}^{1} 3 x - x^{2} d x

d er i v a t i v e 2 ln (x) + 6

\frac{\partial}{\partial x} (x y - x - y + 1)