derivative of xsec^2(pix)

解

\frac{d}{d x} (x sec^{2} (π x))

sec^{2} (π x) + 2 π x sec^{2} (π x) tan (π x)

解答ステップ

\frac{d}{d x} (x sec^{2} (π x))

積の法則を適用:

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

f = x, g = sec^{2} (π x)

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

\frac{d x}{d x} = 1

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

= 1 \cdot sec^{2} (π x) + 2 π sec^{2} (π x) tan (π x) x

簡素化

= sec^{2} (π x) + 2 π x sec^{2} (π x) tan (π x)