derivative of e^{6x}cos(bx)

Lösung

\frac{d}{d x} (e^{6 x} cos (b x))

6 e^{6 x} cos (b x) - b e^{6 x} sin (b x)

Schritte zur Lösung

\frac{d}{d x} (e^{6 x} cos (b x))

Wende die Produktregel an:

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

f = e^{6 x}, g = cos (b x)

= \frac{d}{d x} (e^{6 x}) cos (b x) + \frac{d}{d x} (cos (b x)) e^{6 x}

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

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

= e^{6 x} \cdot 6 cos (b x) + (- sin (b x) b) e^{6 x}

Vereinfache

= 6 e^{6 x} cos (b x) - b e^{6 x} sin (b x)

d er i v a t i v e (x + y)^{2} - 4 x + y + 10

\int_{0}^{π} 2 cos^{2} (\frac{π}{2}) d x

\int \frac{2}{7} x^{2} + 1 d x

t an g e n t f (x) = 3 x^{2}, (- 1, 3)

l a pl a ce t r an s f or m g (t) = t