(\partial)/(\partial x)(U(x)(1+(R(x)^3)/(x^3)))

Lösung

\frac{\partial}{\partial x} (U (x) (1 + \frac{R ( x ) ( x ) ^{3}}{x ^{3}}))

\frac{\partial}{\partial x} (U (x)) (1 + R (x)) + \frac{\partial}{\partial x} (R (x)) U (x)

Schritte zur Lösung

\frac{\partial}{\partial x} (U (x) (1 + \frac{R ( x ) ( x ) ^{3}}{x ^{3}}))

Vereinfache

U (x) (1 + \frac{R ( x ) ( x ) ^{3}}{x ^{3}}) : U (x) (1 + R (x))

= \frac{\partial}{\partial x} (U (x) (1 + R (x)))

Wende die Produktregel an:

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

f = U (x), g = 1 + R (x)

= \frac{\partial}{\partial x} (U (x)) (1 + R (x)) + \frac{\partial}{\partial x} (1 + R (x)) U (x)

\frac{\partial}{\partial x} (1 + R (x)) = \frac{\partial}{\partial x} (R (x))

= \frac{\partial}{\partial x} (U (x)) (1 + R (x)) + \frac{\partial}{\partial x} (R (x)) U (x)

a re a 2 x + y^{2} = 48, x = y

y^{^{'}} + 3 y = 4 sin (e^{3 x})

\int \frac{13}{25 - 9 x ^{2}} d x

d er i v a t i v e \frac{( 2 x ^{2} + 3 x )}{4 x ^{2}}

\frac{d}{d x} (a x sin (2 x) + b x cos (2 x))