(\partial)/(\partial x)((4x-y^2)^{3/2})

Lösung

\frac{\partial}{\partial x} ((4 x - y^{2})^{\frac{3}{2}})

6 (4 x - y^{2})^{\frac{1}{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} ((4 x - y^{2})^{\frac{3}{2}})

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{3 ( 4 x - y ^{2} ) ^{\frac{1}{2}}}{2} \frac{\partial}{\partial x} (4 x - y^{2})

= \frac{3 ( 4 x - y ^{2} ) ^{\frac{1}{2}}}{2} \frac{\partial}{\partial x} (4 x - y^{2})

\frac{\partial}{\partial x} (4 x - y^{2}) = 4

= \frac{3 ( 4 x - y ^{2} ) ^{\frac{1}{2}}}{2} \cdot 4

Vereinfache

\frac{3 ( 4 x - y ^{2} ) ^{\frac{1}{2}}}{2} \cdot 4 : 6 (4 x - y^{2})^{\frac{1}{2}}

= 6 (4 x - y^{2})^{\frac{1}{2}}

n = 1 \sum \infty \frac{6}{2 ^{n}}

\frac{\partial}{\partial x} (y (1 - x))

in v erse l a pl a ce e^{- 3 s} \cdot \frac{5}{4 s ^{2} + 16}

t an g e n t 4 x - x^{2} (1.3)

\frac{d}{d x} (ln (e^{x} + e^{- x}))