derivative of (x^3+1^{1/2})

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{2 ( x ^{3} + 1 ) ^{\frac{1}{2}}} \cdot 3 x^{2} : \frac{3 x ^{2}}{2 ( x ^{3} + 1 ) ^{\frac{1}{2}}}

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

\frac{d}{d x} (sin (x) sin (2 x))

\frac{d}{d x} (3 x^{4} - 16 x^{3} - 18 x^{2})

d er i v a t i v e 10 x + 1

d er i v a t i v e y = [x (x^{5} + 4)^{4}]

\int \frac{6}{3 x + 1} d x