derivative f(x)=tan(x)sin(6x^3)

解

導関数

f (x) = tan (x) sin (6 x^{3})

sec^{2} (x) sin (6 x^{3}) + cos (6 x^{3}) \cdot 18 x^{2} tan (x)

解答ステップ

\frac{d}{d x} (tan (x) sin (6 x^{3}))

積の法則を適用:

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

f = tan (x), g = sin (6 x^{3})

= \frac{d}{d x} (tan (x)) sin (6 x^{3}) + \frac{d}{d x} (sin (6 x^{3})) tan (x)

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

\frac{d}{d x} (sin (6 x^{3})) = cos (6 x^{3}) \cdot 18 x^{2}

= sec^{2} (x) sin (6 x^{3}) + cos (6 x^{3}) \cdot 18 x^{2} tan (x)