implicit (dy)/(dx),y=(sin(x))^{6x}

解

暗黙的な導関数

\frac{d y}{d x}, y = (sin (x))^{6 x}

\frac{d y}{d x} = 6 sin^{6 x} (x) (ln (sin (x)) + x cot (x))

解答ステップ

y = (sin (x))^{6 x}

y

を

y (x) として扱う

両側を計算:

\frac{d y}{d x} = 6 sin^{6 x} (x) (ln (sin (x)) + x cot (x))

分離する

\frac{d y}{d x} : \frac{d y}{d x} = 6 sin^{6 x} (x) (ln (sin (x)) + x cot (x))

\frac{d y}{d x} = 6 sin^{6 x} (x) (ln (sin (x)) + x cot (x))