derivative f(x)=cos(sqrt(sin(tan(pix))))

解

導関数

f (x) = cos (sin (tan (π x)))

- \frac{π sec ^{2} ( π x ) cos ( tan ( π x ) ) sin ( sin ( tan ( π x ) ) )}{2 sin ( tan ( π x ) )}

解答ステップ

\frac{d}{d x} (cos (sin (tan (π x))))

連鎖法則を適用:

- sin (sin (tan (π x))) \frac{d}{d x} (sin (tan (π x)))

= - sin (sin (tan (π x))) \frac{d}{d x} (sin (tan (π x)))

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

= - sin (sin (tan (π x))) \frac{π sec ^{2} ( π x ) cos ( tan ( π x ) )}{2 sin ( tan ( π x ) )}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{π sec ^{2} ( π x ) cos ( tan ( π x ) ) sin ( sin ( tan ( π x ) ) )}{2 sin ( tan ( π x ) )}