derivative of x^3(ln(x)^{cos(x)})

Lösung

\frac{d}{d x} (x^{3} (ln (x))^{c o s (x)})

3 x^{2} ln^{c o s (x)} (x) + x^{3} ln^{c o s (x)} (x) (- sin (x) ln (ln (x)) + \frac{cos ( x )}{x ln ( x )})

Schritte zur Lösung

\frac{d}{d x} (x^{3} (ln (x))^{c o s (x)})

Wende die Produktregel an:

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

f = x^{3}, g = (ln (x))^{c o s (x)}

= \frac{d}{d x} (x^{3}) (ln (x))^{c o s (x)} + \frac{d}{d x} ((ln (x))^{c o s (x)}) x^{3}

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

\frac{d}{d x} ((ln (x))^{c o s (x)}) = ln^{c o s (x)} (x) (- sin (x) ln (ln (x)) + \frac{cos ( x )}{x ln ( x )})

= 3 x^{2} (ln (x))^{c o s (x)} + ln^{c o s (x)} (x) (- sin (x) ln (ln (x)) + \frac{cos ( x )}{x ln ( x )}) x^{3}

Vereinfache

= 3 x^{2} ln^{c o s (x)} (x) + x^{3} ln^{c o s (x)} (x) (- sin (x) ln (ln (x)) + \frac{cos ( x )}{x ln ( x )})

\int y^{- 4} d y

t an g e n t f (x) = \frac{3}{( x + 5 ) ^{2}}, at x = \frac{3}{16}

\frac{\partial}{\partial y} (\frac{5 x}{6 y})

(cot (x))^{^{'}}

\frac{\partial}{\partial x} (tan (3 x - 4 y))