(\partial)/(\partial y)(4x^{0.5}+2y^{0.25})

Lösung

\frac{\partial}{\partial y} (4 x^{0.5} + 2 y^{0.25})

\frac{0.5}{y ^{0.75}}

Schritte zur Lösung

\frac{\partial}{\partial y} (4 x^{0.5} + 2 y^{0.25})

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (4 x^{0.5}) + \frac{\partial}{\partial y} (2 y^{0.25})

\frac{\partial}{\partial y} (4 x^{0.5}) = 0

\frac{\partial}{\partial y} (2 y^{0.25}) = \frac{0.5}{y ^{0.75}}

= 0 + \frac{0.5}{y ^{0.75}}

Vereinfache

= \frac{0.5}{y ^{0.75}}

\frac{\partial}{\partial y} (ln (x yz))

\int 7^{x^{2}} d x

x \to \infty lim (\frac{1}{x} + 1)

t an g e n t y^{3} x + y^{2} x^{2} = 6, (2, 1)

y^{^{''}} - 2 y^{^{'}} + 7 y = 0