derivative of 3x(sin(x+cos(x)))

Lösung

\frac{d}{d x} (3 x (sin (x) + cos (x)))

3 (sin (x) + cos (x) + x (cos (x) - sin (x)))

Schritte zur Lösung

\frac{d}{d x} (3 x (sin (x) + cos (x)))

Entferne die Konstante:

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

= 3 \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)

= 3 (\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)

= 3 (1 \cdot (sin (x) + cos (x)) + (cos (x) - sin (x)) x)

Vereinfache

= 3 (sin (x) + cos (x) + x (cos (x) - sin (x)))

\frac{\partial}{\partial x} (x ln (z^{6} + x^{4}))

l a pl a ce t r an s f or m 2 \cdot e^{(5 \cdot t - 2)}

\int_{\frac{1}{7}}^{5} 10 x ln (7 x) d x

\frac{d}{d t} (1 - 3 t)

ma c l a u r in x e^{- x^{2}}