derivative sin(x)*tan(x)

Lösung

ableitung von

sin (x) \cdot tan (x)

sin (x) (1 + sec^{2} (x))

Schritte zur Lösung

\frac{d}{d x} (sin (x) tan (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (x), g = tan (x)

= \frac{d}{d x} (sin (x)) tan (x) + \frac{d}{d x} (tan (x)) sin (x)

\frac{d}{d x} (sin (x)) = cos (x)

\frac{d}{d x} (tan (x)) = sec^{2} (x)

= cos (x) tan (x) + sec^{2} (x) sin (x)

Vereinfache

cos (x) tan (x) + sec^{2} (x) sin (x) : sin (x) (1 + sec^{2} (x))

= sin (x) (1 + sec^{2} (x))

a re a f (x) = x^{5} + 4, g (x) = x + 4

t an g e n t f (x) = - \frac{1}{2 1 - x}, at x = - 8

f^{^{'}} (x) = \frac{8 x ^{5} - 6 x ^{9}}{x ^{4}}

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

\int π sin (8 π x) d x