derivative of x/({z(x)})

Lösung

\frac{d}{d x} (\frac{x}{z ( x )})

\frac{z ( x ) - x \frac{d}{d x} ( z ( x ) )}{z ( x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{z ( x )})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d x}{d x} z ( x ) - \frac{d}{d x} ( z ( x ) ) x}{z ( x ) ^{2}}

\frac{d x}{d x} = 1

= \frac{1 \cdot z ( x ) - \frac{d}{d x} ( z ( x ) ) x}{z ( x ) ^{2}}

Vereinfache

= \frac{z ( x ) - x \frac{d}{d x} ( z ( x ) )}{z ( x ) ^{2}}

\frac{\partial}{\partial x} (14 x y e^{- x^{2} - y^{2}})

t an g e n t f (x) = x + 3, at x = 6

y^{^{''}} + 16 y = 6 tan (4 x)

im pl i c i t \frac{d y}{d x}, x e^{y} - 10 x + 3 y = 0

d er i v a t i v e (sin (3 x))^{l n (x)}