derivative of x^9ln(5x)

Lösung

\frac{d}{d x} (x^{9} ln (5 x))

9 x^{8} ln (5 x) + x^{8}

Schritte zur Lösung

\frac{d}{d x} (x^{9} ln (5 x))

Wende die Produktregel an:

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

f = x^{9}, g = ln (5 x)

= \frac{d}{d x} (x^{9}) ln (5 x) + \frac{d}{d x} (ln (5 x)) x^{9}

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

\frac{d}{d x} (ln (5 x)) = \frac{1}{x}

= 9 x^{8} ln (5 x) + \frac{1}{x} x^{9}

\frac{1}{x} x^{9} = x^{8}

= 9 x^{8} ln (5 x) + x^{8}

y y^{^{'}} + 3 y = x^{2} y

in v erse l a pl a ce (\frac{20}{10 s + 1}) \cdot \frac{1}{s}

t an g e n t f (x) = ln (e^{x^{2}}), at x = 1

\int \frac{2 x + 5}{x ^{2} + 2 x + 5} d x

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