derivative f(x)=x^{2cos(x)}

Lösung

ableitung von

f (x) = x^{2 c o s (x)}

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

Schritte zur Lösung

\frac{d}{d x} (x^{2 c o s (x)})

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

x^{2 c o s (x)} = e^{2 c o s (x) l n (x)}

= \frac{d}{d x} (e^{2 c o s (x) l n (x)})

Wende die Kettenregel an:

e^{2 c o s (x) l n (x)} \frac{d}{d x} (2 cos (x) ln (x))

= e^{2 c o s (x) l n (x)} \frac{d}{d x} (2 cos (x) ln (x))

\frac{d}{d x} (2 cos (x) ln (x)) = 2 (- sin (x) ln (x) + \frac{cos ( x )}{x})

= e^{2 c o s (x) l n (x)} \cdot 2 (- sin (x) ln (x) + \frac{cos ( x )}{x})

e^{2 c o s (x) l n (x)} = x^{2 c o s (x)}

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

\frac{\partial}{\partial y} (4 x^{2 y})

\frac{d ^{2} y}{d x ^{2}} = x

t an g e n t f (x) = \frac{x}{x ^{2} + 1}

\frac{d}{d x} (\frac{cot ( x )}{1 + cot ( x )})

im pl i c i t \frac{d y}{d x}, y - 5 x y^{3} + 8 = 5 sin (y^{3} + 2 x^{2})