derivative of x^4tan(x-sqrt(x))

解

\frac{d}{d x} (x^{4} tan (x) - x)

4 x^{3} tan (x) + sec^{2} (x) x^{4} - \frac{1}{2 x}

解答ステップ

\frac{d}{d x} (x^{4} tan (x) - x)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{4} tan (x)) - \frac{d}{d x} (x)

\frac{d}{d x} (x^{4} tan (x)) = 4 x^{3} tan (x) + sec^{2} (x) x^{4}

\frac{d}{d x} (x) = \frac{1}{2 x}

= 4 x^{3} tan (x) + sec^{2} (x) x^{4} - \frac{1}{2 x}