derivative f(x)=(2x^2tan(x))/(sec(x))

解

導関数

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

2 (x^{2} cos (x) + 2 x sin (x))

解答ステップ

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

簡素化

\frac{2 x ^{2} tan ( x )}{sec ( x )} : 2 x^{2} tan (x) cos (x)

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

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

積の法則を適用:

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

f = x^{2}, g = tan (x) cos (x)

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

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

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

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

cos (x) tan (x) = sin (x)

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