derivative (sin(x)+2tan(x))(sec(x)-3csc(x))

Lösung

ableitung von

(sin (x) + 2 tan (x)) (sec (x) - 3 csc (x))

(cos (x) + 2 sec^{2} (x)) (sec (x) - 3 csc (x)) + (sec (x) tan (x) + 3 cot (x) csc (x)) (sin (x) + 2 tan (x))

Schritte zur Lösung

\frac{d}{d x} ((sin (x) + 2 tan (x)) (sec (x) - 3 csc (x)))

Wende die Produktregel an:

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

f = sin (x) + 2 tan (x), g = sec (x) - 3 csc (x)

= \frac{d}{d x} (sin (x) + 2 tan (x)) (sec (x) - 3 csc (x)) + \frac{d}{d x} (sec (x) - 3 csc (x)) (sin (x) + 2 tan (x))

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

\frac{d}{d x} (sec (x) - 3 csc (x)) = sec (x) tan (x) + 3 cot (x) csc (x)

= (cos (x) + 2 sec^{2} (x)) (sec (x) - 3 csc (x)) + (sec (x) tan (x) + 3 cot (x) csc (x)) (sin (x) + 2 tan (x))

\frac{d}{d x} (\frac{1}{x ^{12}})

d er i v a t i v e tan (2 x^{2} - x + 3)

d er i v a t i v e y = 9 sec (\frac{1}{3} x)

f (x) = 2 x ln (x) + x

\int (\frac{5 - 10 x ^{2}}{4 x ^{3} - 6 x + 15}) d x