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Beliebt Rechnen >

derivative y=e^{4cos(sqrt(x))}

Lösung

ableitung von

y = e^{4 c o s (x)}

Lösung

- \frac{2 e ^{4 c o s (x)} sin ( x )}{x}

Schritte zur Lösung

\frac{d}{d x} (e^{4 c o s (x)})

Wende die Kettenregel an:

e^{4 c o s (x)} \frac{d}{d x} (4 cos (x))

= e^{4 c o s (x)} \frac{d}{d x} (4 cos (x))

\frac{d}{d x} (4 cos (x)) = - \frac{2 sin ( x )}{x}

= e^{4 c o s (x)} (- \frac{2 sin ( x )}{x})

Vereinfache

e^{4 c o s (x)} (- \frac{2 sin ( x )}{x}) : - \frac{2 e ^{4 c o s (x)} sin ( x )}{x}

= - \frac{2 e ^{4 c o s (x)} sin ( x )}{x}

Graph

Beliebte Beispiele

limit as h approaches 0 of sin(1/h)

h \to 0 lim (sin (\frac{1}{h}))

integral of 2sin^3(2x)cos^3(2x)

\int 2 sin^{3} (2 x) cos^{3} (2 x) d x

limit as x approaches+10 of x

x \to + 10 lim (x)

(dy)/(dx)=x^6y^{-7},y(0)=4

\frac{d y}{d x} = x^{6} y^{- 7}, y (0) = 4

derivative of arcsin(cos(x))

\frac{d}{d x} (arcsin (cos (x)))