(\partial)/(\partial x)(x^{0.25}Y(x)^{0.5})

Lösung

\frac{\partial}{\partial x} (x^{0.25} Y (x) (x)^{0.5})

0.75 x^{\frac{1}{2} - 0.75} Y (x) + \frac{\partial}{\partial x} (Y (x)) x^{0.25 + \frac{1}{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{0.25} Y (x) (x)^{0.5})

Vereinfache

x^{0.25} Y (x) (x)^{0.5} : x^{0.25 + \frac{1}{2}} Y (x)

= \frac{\partial}{\partial x} (x^{0.25 + \frac{1}{2}} Y (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{0.25 + \frac{1}{2}}, g = Y (x)

= \frac{\partial}{\partial x} (x^{0.25 + \frac{1}{2}}) Y (x) + \frac{\partial}{\partial x} (Y (x)) x^{0.25 + \frac{1}{2}}

\frac{\partial}{\partial x} (x^{0.25 + \frac{1}{2}}) = 0.75 x^{\frac{1}{2} - 0.75}

= 0.75 x^{\frac{1}{2} - 0.75} Y (x) + \frac{\partial}{\partial x} (Y (x)) x^{0.25 + \frac{1}{2}}

t an g e n t 2 x^{2} - x - 3

in v erse l a pl a ce \frac{1}{( s ^{2} + 0.2 s + 1 ) s}

x \to - 3 lim (x^{2} + 3 x + 1)

t a y l or cos (π x) \frac{1}{2}

\int x tan^{2} (x) d x