derivative y=7^{x+arccos(x)}

Lösung

ableitung von

y = 7^{x + a r c c o s (x)}

ln (7) \cdot 7^{x + a r c c o s (x)} (1 - \frac{1}{1 - x ^{2}})

Schritte zur Lösung

\frac{d}{d x} (7^{x + a r c c o s (x)})

Wende Exponentenregel an:

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

7^{x + a r c c o s (x)} = e^{(x + a r c c o s (x)) l n (7)}

= \frac{d}{d x} (e^{(x + a r c c o s (x)) l n (7)})

Wende die Kettenregel an:

e^{(x + a r c c o s (x)) l n (7)} \frac{d}{d x} ((x + arccos (x)) ln (7))

= e^{(x + a r c c o s (x)) l n (7)} \frac{d}{d x} ((x + arccos (x)) ln (7))

\frac{d}{d x} ((x + arccos (x)) ln (7)) = ln (7) (1 - \frac{1}{1 - x ^{2}})

= e^{(x + a r c c o s (x)) l n (7)} ln (7) (1 - \frac{1}{1 - x ^{2}})

e^{(x + a r c c o s (x)) l n (7)} = 7^{x + a r c c o s (x)}

= ln (7) \cdot 7^{x + a r c c o s (x)} (1 - \frac{1}{1 - x ^{2}})

a re a x^{2} - 4 x, 2 x - x^{2}

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\frac{d}{d x} (ln (2 + e^{x}))

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\frac{\partial}{\partial z} (2 x yz)