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

Lösung

ableitung von

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)))

\frac{d}{d θ} (2 sin (2 θ))

t an g e n t f (x) = 6 + 5 x^{2} - 2 x^{3}, at x = 1

\frac{d}{d x} (x^{2} + 2 x y)

n = 0 \sum \infty (\frac{e}{4 π})^{n}

\int \frac{x ^{2} + 5 x + 4}{x ^{2} - 2 x + 1} d x