derivative f(x)=5x(sin(x)+cos(x))

Lösung

ableitung von

f (x) = 5 x (sin (x) + cos (x))

5 (sin (x) + cos (x) + x (cos (x) - sin (x)))

Schritte zur Lösung

\frac{d}{d x} (5 x (sin (x) + cos (x)))

Entferne die Konstante:

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

= 5 \frac{d}{d x} (x (sin (x) + cos (x)))

Wende die Produktregel an:

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

f = x, g = sin (x) + cos (x)

= 5 (\frac{d x}{d x} (sin (x) + cos (x)) + \frac{d}{d x} (sin (x) + cos (x)) x)

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

\frac{d}{d x} (sin (x) + cos (x)) = cos (x) - sin (x)

= 5 (1 \cdot (sin (x) + cos (x)) + (cos (x) - sin (x)) x)

Vereinfache

= 5 (sin (x) + cos (x) + x (cos (x) - sin (x)))

\int sin (π + 2 y) - sin (2 y) d y

\frac{\partial}{\partial y} (x y e^{y} + e^{y} sin (x))

\frac{\partial}{\partial x} (16 - x^{2} - y^{2})

a re a y = e^{- 2 x} + 1, y = 0, x = 0, x = 3

\frac{\partial}{\partial t} (3 e^{s i n (x + 4 c t)})