derivative y=16^{sin(x^2)}

Lösung

ableitung von

y = 1 6^{s i n (x^{2})}

ln (2) \cdot 2^{4 s i n (x^{2}) + 3} x cos (x^{2})

Schritte zur Lösung

\frac{d}{d x} (1 6^{s i n (x^{2})})

Wende Exponentenregel an:

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

1 6^{s i n (x^{2})} = e^{s i n (x^{2}) l n (16)}

= \frac{d}{d x} (e^{s i n (x^{2}) l n (16)})

Wende die Kettenregel an:

e^{s i n (x^{2}) l n (16)} \frac{d}{d x} (sin (x^{2}) ln (16))

= e^{s i n (x^{2}) l n (16)} \frac{d}{d x} (sin (x^{2}) ln (16))

\frac{d}{d x} (sin (x^{2}) ln (16)) = 8 ln (2) x cos (x^{2})

= e^{s i n (x^{2}) l n (16)} \cdot 8 ln (2) x cos (x^{2})

Vereinfache

e^{s i n (x^{2}) l n (16)} \cdot 8 ln (2) x cos (x^{2}) : ln (2) \cdot 2^{4 s i n (x^{2}) + 3} x cos (x^{2})

= ln (2) \cdot 2^{4 s i n (x^{2}) + 3} x cos (x^{2})

s l o p e (2.3) (- 2.3)

\int \frac{x ^{5} - 9 x ^{3} - 9 x ^{2} - 9}{x ^{3} + 9 x} d x

d er i v a t i v e f (x) = tan (\frac{3 π}{4} x)

x \to 3 - lim (arcsin (\frac{x}{3}))

\int 15 sin^{2} (x) d x