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Beliebt Rechnen >

derivative of sin^5(3x)

Lösung

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

Lösung

15 sin^{4} (3 x) cos (3 x)

Schritte zur Lösung

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

Wende die Kettenregel an:

5 (sin (3 x))^{4} \frac{d}{d x} (sin (3 x))

= 5 (sin (3 x))^{4} \frac{d}{d x} (sin (3 x))

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

= 5 (sin (3 x))^{4} cos (3 x) \cdot 3

Vereinfache

= 15 sin^{4} (3 x) cos (3 x)

Graph

Beliebte Beispiele

y^'=4-9x^2-6x^5

y^{^{'}} = 4 - 9 x^{2} - 6 x^{5}

derivative of cos(x+sin(x)+1/2 x^2+1/x)

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

integral of (3^x+2/x)

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

integral from 2 to 5 of 1/(sqrt(x-1))

\int_{2}^{5} \frac{1}{x - 1} d x

integral of x/k

\int \frac{x}{k} d x