derivative of 4^{(8x^4+cos(x)^3})

Lösung

\frac{d}{d x} (4^{(8 x^{4} + c o s (x))^{3}})

3 ln (2) \cdot 2^{2 (8 x^{4} + c o s (x))^{3} + 1} (8 x^{4} + cos (x))^{2} (32 x^{3} - sin (x))

Schritte zur Lösung

\frac{d}{d x} (4^{(8 x^{4} + c o s (x))^{3}})

Wende Exponentenregel an:

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

4^{(8 x^{4} + c o s (x))^{3}} = e^{(8 x^{4} + c o s (x))^{3} l n (4)}

= \frac{d}{d x} (e^{(8 x^{4} + c o s (x))^{3} l n (4)})

Wende die Kettenregel an:

e^{(8 x^{4} + c o s (x))^{3} l n (4)} \frac{d}{d x} ((8 x^{4} + cos (x))^{3} ln (4))

= e^{(8 x^{4} + c o s (x))^{3} l n (4)} \frac{d}{d x} ((8 x^{4} + cos (x))^{3} ln (4))

\frac{d}{d x} ((8 x^{4} + cos (x))^{3} ln (4)) = 6 ln (2) (8 x^{4} + cos (x))^{2} (32 x^{3} - sin (x))

= e^{(8 x^{4} + c o s (x))^{3} l n (4)} \cdot 6 ln (2) (8 x^{4} + cos (x))^{2} (32 x^{3} - sin (x))

Vereinfache

e^{(8 x^{4} + c o s (x))^{3} l n (4)} \cdot 6 ln (2) (8 x^{4} + cos (x))^{2} (32 x^{3} - sin (x)) : 3 ln (2) \cdot 2^{2 (8 x^{4} + c o s (x))^{3} + 1} (8 x^{4} + cos (x))^{2} (32 x^{3} - sin (x))

= 3 ln (2) \cdot 2^{2 (8 x^{4} + c o s (x))^{3} + 1} (8 x^{4} + cos (x))^{2} (32 x^{3} - sin (x))

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