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Beliebt Rechnen >

derivative of (cos(7x)^x)

Lösung

\frac{d}{d x} ((cos (7 x))^{x})

Lösung

cos^{x} (7 x) (ln (cos (7 x)) - 7 x tan (7 x))

Schritte zur Lösung

\frac{d}{d x} ((cos (7 x))^{x})

Wende Exponentenregel an:

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

(cos (7 x))^{x} = e^{x l n (c o s (7 x))}

= \frac{d}{d x} (e^{x l n (c o s (7 x))})

Wende die Kettenregel an:

e^{x l n (c o s (7 x))} \frac{d}{d x} (x ln (cos (7 x)))

= e^{x l n (c o s (7 x))} \frac{d}{d x} (x ln (cos (7 x)))

\frac{d}{d x} (x ln (cos (7 x))) = ln (cos (7 x)) - 7 x tan (7 x)

= e^{x l n (c o s (7 x))} (ln (cos (7 x)) - 7 x tan (7 x))

e^{x l n (c o s (7 x))} = cos^{x} (7 x)

= cos^{x} (7 x) (ln (cos (7 x)) - 7 x tan (7 x))

Graph

Beliebte Beispiele

fläche sqrt(x), 1/2 x,0,25

a re a x, \frac{1}{2} x, 0, 25

(\partial)/(\partial x)((3x-y)/(3x+y))

\frac{\partial}{\partial x} (\frac{3 x - y}{3 x + y})

integral of x(2x-1)^9

\int x (2 x - 1)^{9} d x

derivative of \sqrt[8]{x}-8e^x

\frac{d}{d x} (8 x - 8 e^{x})

tangent f(x)=x^2-9,(4,7)

t an g e n t f (x) = x^{2} - 9, (4, 7)