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Beliebt Rechnen >

derivative of 5sin(x+xcos(x))

Lösung

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

Lösung

6 cos (x) - x sin (x)

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Vereinfache

= 6 cos (x) - x sin (x)

Graph

Beliebte Beispiele

(d^2S)/(dx^2)=x

\frac{d ^{2} S}{d x ^{2}} = x

derivative of 3x^5-5x^3

\frac{d}{d x} (3 x^{5} - 5 x^{3})

integral from 2 to infinity of-7x^{-2}

\int_{2}^{\infty} - 7 x^{- 2} d x

derivative of (x/3 ^3)

\frac{d}{d x} ((\frac{x}{3})^{3})

derivative of (x^2+2x-4/((x+1)^2))

\frac{d}{d x} (\frac{x ^{2} + 2 x - 4}{( x + 1 ) ^{2}})