derivative f(x)= 1/16 x^4+1/(2x^2)

Lösung

ableitung von

f (x) = \frac{1}{16} x^{4} + \frac{1}{2 x ^{2}}

\frac{x ^{3}}{4} - \frac{1}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{16} x^{4} + \frac{1}{2 x ^{2}})

Vereinfache

\frac{1}{16} x^{4} + \frac{1}{2 x ^{2}} : \frac{x ^{4}}{16} + \frac{1}{2 x ^{2}}

= \frac{d}{d x} (\frac{x ^{4}}{16} + \frac{1}{2 x ^{2}})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{x ^{4}}{16}) + \frac{d}{d x} (\frac{1}{2 x ^{2}})

\frac{d}{d x} (\frac{x ^{4}}{16}) = \frac{x ^{3}}{4}

\frac{d}{d x} (\frac{1}{2 x ^{2}}) = - \frac{1}{x ^{3}}

= \frac{x ^{3}}{4} - \frac{1}{x ^{3}}

d er i v a t i v e f (x) = tan (x)

p o l a r (3, 4)

θ = \frac{5 π}{3}

d er i v a t i v e y = (cos (x))^{x}

p o l a r (3, - 2)