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Beliebt Rechnen >

derivative of sin^2(e^{3x+1})

Lösung

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

Lösung

6 e^{3 x + 1} sin (e^{3 x + 1}) cos (e^{3 x + 1})

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (sin (e^{3 x + 1})) = cos (e^{3 x + 1}) e^{3 x + 1} \cdot 3

= 2 sin (e^{3 x + 1}) cos (e^{3 x + 1}) e^{3 x + 1} \cdot 3

Vereinfache

= 6 e^{3 x + 1} sin (e^{3 x + 1}) cos (e^{3 x + 1})

Graph

Beliebte Beispiele

sum from n=0 to infinity of (3^n)/(3^n)

n = 0 \sum \infty \frac{3 ^{n}}{3 ^{n}}

integral of (x^3)/(x^4-3)

\int \frac{x ^{3}}{x ^{4} - 3} d x

integral from 0 to 2 of x^2-1

\int_{0}^{2} x^{2} - 1 d x

f (x) = - ln (x)

integral of 5x^{-3}

\int 5 x^{- 3} d x