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Beliebt Rechnen >

derivative y=x^{-8cos(x)}

Lösung

ableitung von

y = x^{- 8 c o s (x)}

Lösung

x^{- 8 c o s (x)} (8 sin (x) ln (x) - \frac{8 cos ( x )}{x})

Schritte zur Lösung

\frac{d}{d x} (x^{- 8 c o s (x)})

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

x^{- 8 c o s (x)} = e^{(- 8 c o s (x)) l n (x)}

= \frac{d}{d x} (e^{(- 8 c o s (x)) l n (x)})

Wende die Kettenregel an:

e^{(- 8 c o s (x)) l n (x)} \frac{d}{d x} ((- 8 cos (x)) ln (x))

= e^{(- 8 c o s (x)) l n (x)} \frac{d}{d x} ((- 8 cos (x)) ln (x))

\frac{d}{d x} ((- 8 cos (x)) ln (x)) = 8 sin (x) ln (x) - \frac{8 cos ( x )}{x}

= e^{(- 8 c o s (x)) l n (x)} (8 sin (x) ln (x) - \frac{8 cos ( x )}{x})

Vereinfache

e^{(- 8 c o s (x)) l n (x)} (8 sin (x) ln (x) - \frac{8 cos ( x )}{x}) : x^{- 8 c o s (x)} (8 sin (x) ln (x) - \frac{8 cos ( x )}{x})

= x^{- 8 c o s (x)} (8 sin (x) ln (x) - \frac{8 cos ( x )}{x})

Graph

Beliebte Beispiele

tangent y=sin(t)+1/6 e^t,(pi, 1/6 e^pi)

t an g e n t y = sin (t) + \frac{1}{6} e^{t}, (π, \frac{1}{6} e^{π})

derivative of y=x^4*x^5

\frac{d}{d x} y = x^{4} \cdot x^{5}

integral of ((x^2+1))/((x-8)(x-7)^2)

\int \frac{( x ^{2} + 1 )}{( x - 8 ) ( x - 7 ) ^{2}} d x

derivative of x(x^2+x+1^3)

\frac{d}{d x} (x (x^{2} + x + 1)^{3})

integral of sqrt(t^2+t)

\int t^{2} + t d t