(\partial)/(\partial x)((4x+3)/(4y+1))

Lösung

\frac{\partial}{\partial x} (\frac{4 x + 3}{4 y + 1})

\frac{4}{4 y + 1}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{4 x + 3}{4 y + 1})

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{4 y + 1} \frac{\partial}{\partial x} (4 x + 3)

Wende die Summen-/Differenzregel an:

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

= \frac{1}{4 y + 1} (\frac{\partial}{\partial x} (4 x) + \frac{\partial}{\partial x} (3))

\frac{\partial}{\partial x} (4 x) = 4

\frac{\partial}{\partial x} (3) = 0

= \frac{1}{4 y + 1} (4 + 0)

Vereinfache

\frac{1}{4 y + 1} (4 + 0) : \frac{4}{4 y + 1}

= \frac{4}{4 y + 1}

\frac{d}{d x} (\frac{ln ( x )}{x ^{\frac{5}{4}}})

\int y cos (y) sin^{2} (y) d y

t an g e n t \frac{1}{x}, at x = 2

a re a y = e^{x}, y = e^{3 x}, x = ln (2), x = ln (3)

d er i v a t i v e [x + (x + sin^{2} (x))^{5}]^{7}