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Beliebt Rechnen >

derivative of x-ln(e^xcos(x))

Lösung

\frac{d}{d x} (x - ln (e^{x} cos (x)))

Lösung

tan (x)

Schritte zur Lösung

\frac{d}{d x} (x - ln (e^{x} cos (x)))

Wende die Summen-/Differenzregel an:

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

= \frac{d x}{d x} - \frac{d}{d x} (ln (e^{x} cos (x)))

\frac{d x}{d x} = 1

\frac{d}{d x} (ln (e^{x} cos (x))) = 1 - tan (x)

= 1 - (1 - tan (x))

Vereinfache

= tan (x)

Graph

Beliebte Beispiele

derivative of 1/(sqrt(2)x)

\frac{d}{d x} (\frac{1}{2} x)

derivative f(x)=\sqrt[4]{x^3}

d er i v a t i v e f (x) = 4 x^{3}

derivative of (x^2/(2sqrt(x)+1))

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

d/(dy)(x^2-y^2)

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

sum from n=1 to infinity of n/(n^3+2)

n = 1 \sum \infty \frac{n}{n ^{3} + 2}