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Beliebt Rechnen >

derivative of (x^4+8^{1/2})

Lösung

\frac{d}{d x} ((x^{4} + 8)^{\frac{1}{2}})

Lösung

\frac{2 x ^{3}}{( x ^{4} + 8 ) ^{\frac{1}{2}}}

Schritte zur Lösung

\frac{d}{d x} ((x^{4} + 8)^{\frac{1}{2}})

Wende die Kettenregel an:

\frac{1}{2 ( x ^{4} + 8 ) ^{\frac{1}{2}}} \frac{d}{d x} (x^{4} + 8)

= \frac{1}{2 ( x ^{4} + 8 ) ^{\frac{1}{2}}} \frac{d}{d x} (x^{4} + 8)

\frac{d}{d x} (x^{4} + 8) = 4 x^{3}

= \frac{1}{2 ( x ^{4} + 8 ) ^{\frac{1}{2}}} \cdot 4 x^{3}

Vereinfache

\frac{1}{2 ( x ^{4} + 8 ) ^{\frac{1}{2}}} \cdot 4 x^{3} : \frac{2 x ^{3}}{( x ^{4} + 8 ) ^{\frac{1}{2}}}

= \frac{2 x ^{3}}{( x ^{4} + 8 ) ^{\frac{1}{2}}}

Graph

Beliebte Beispiele

(\partial)/(\partial x)(y^{1/3})

\frac{\partial}{\partial x} (y^{\frac{1}{3}})

derivative y= 5/((4x)^{-2)}

d er i v a t i v e y = \frac{5}{( 4 x ) ^{- 2}}

(\partial)/(\partial x)(sec(y))

\frac{\partial}{\partial x} (sec (y))

integral of e^{2x}cos(x/4)

\int e^{2 x} cos (\frac{x}{4}) d x

derivative of x/(2+x)

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