derivative of 5sin(xcos(x))

Lösung

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

5 cos (2 x)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

5 (cos (x) cos (x) + (- sin (x)) sin (x)) : 5 cos (2 x)

= 5 cos (2 x)

d er i v a t i v e sin (10 x)

t a y l or tan (x), - \frac{π}{4}

x^{3} y^{^{'}} + x y = 1

n = 1 \sum \infty \frac{2 + n}{1 - 2 n}

\int \frac{1}{16} d x