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Beliebt Rechnen >

derivative of 4x(sin(x+cos(x)))

Lösung

\frac{d}{d x} (4 x (sin (x) + cos (x)))

Lösung

4 (sin (x) + cos (x) + x (cos (x) - sin (x)))

Schritte zur Lösung

\frac{d}{d x} (4 x (sin (x) + cos (x)))

Entferne die Konstante:

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

= 4 \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)

= 4 (\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)

= 4 (1 \cdot (sin (x) + cos (x)) + (cos (x) - sin (x)) x)

Vereinfache

= 4 (sin (x) + cos (x) + x (cos (x) - sin (x)))

Graph

Beliebte Beispiele

(dy)/(dx)=(x-1)/(y^3)

\frac{d y}{d x} = \frac{x - 1}{y ^{3}}

integral of ((ln(x))^{32})/x

\int \frac{( ln ( x ) ) ^{32}}{x} d x

limit as x approaches 2 of 2x^4-10

x \to 2 lim (2 x^{4} - 10)

(d^2)/(dx^2)(ln(x^2+3x+15))

\frac{d ^{2}}{d x ^{2}} (ln (x^{2} + 3 x + 15))

f (x) = 8 ln (x)