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

解

導関数

(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))

解答ステップ

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

積の法則を適用:

(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))