d/(dy)((x)(x^y+1/(x^2)))

Lösung

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

x^{1 + y} ln (x)

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d y} (x^{y}) = x^{y} ln (x)

\frac{d}{d y} (\frac{1}{x ^{2}}) = 0

= x (x^{y} ln (x) + 0)

Vereinfache

x (x^{y} ln (x) + 0) : x^{1 + y} ln (x)

= x^{1 + y} ln (x)

e x p an d (4 e - 2 x)^{3}

e x p an d \frac{x ^{2} + 2 x - 1}{( x ^{2} - x - 2 ) ^{2}}

s im pl i f y 5 (2 + 3)

s im pl i f y (e^{i t} - e^{- i t})^{5}

s im pl i f y (1 - tan (x)) (cos (2 x))