derivative of (x^2+y^2^{2/3})

Lösung

\frac{d}{d x} ((x^{2} + y^{2})^{\frac{2}{3}})

\frac{2 ( 2 x + 2 y \frac{d y}{d x} )}{3 ( x ^{2} + y ^{2} ) ^{\frac{1}{3}}}

Schritte zur Lösung

\frac{d}{d x} ((x^{2} + y^{2})^{\frac{2}{3}})

Wende die Kettenregel an:

\frac{2}{3 ( x ^{2} + y ^{2} ) ^{\frac{1}{3}}} \frac{d}{d x} (x^{2} + y^{2})

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

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

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

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

d er i v a t i v e f (x) = ln (x^{3} + 5 x + 3)

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

d er i v a t i v e y = - \frac{4}{5 x ^{5}} + \frac{15}{4 x ^{4}}

d er i v a t i v e f (x) = x^{2} + 21

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