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Beliebt Rechnen >

derivative of (sin(2x)^x)

Lösung

\frac{d}{d x} ((sin (2 x))^{x})

Lösung

sin^{x} (2 x) (ln (sin (2 x)) + 2 x cot (2 x))

Schritte zur Lösung

\frac{d}{d x} ((sin (2 x))^{x})

Wende Exponentenregel an:

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

(sin (2 x))^{x} = e^{x l n (s i n (2 x))}

= \frac{d}{d x} (e^{x l n (s i n (2 x))})

Wende die Kettenregel an:

e^{x l n (s i n (2 x))} \frac{d}{d x} (x ln (sin (2 x)))

= e^{x l n (s i n (2 x))} \frac{d}{d x} (x ln (sin (2 x)))

\frac{d}{d x} (x ln (sin (2 x))) = ln (sin (2 x)) + 2 x cot (2 x)

= e^{x l n (s i n (2 x))} (ln (sin (2 x)) + 2 x cot (2 x))

e^{x l n (s i n (2 x))} = sin^{x} (2 x)

= sin^{x} (2 x) (ln (sin (2 x)) + 2 x cot (2 x))

Graph

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integral of 3(5^{1-2x})

\int 3 (5^{1 - 2 x}) d x

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

(\partial)/(\partial x)(x^{0.25}Y(x)^{0.5})

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