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

解答

导数

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 ) )}

求解步骤

\frac{d}{d x} (cos (sin (tan (π x))))

使用连锁律:

- 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 ) )}

分式相乘:

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 ) )}

x \to 4 lim (ln ∣ x - 4 ∣)

x^{3} + 3 y - x y^{^{'}} = 0

x \to \frac{π}{2} lim (tan^{2} (x))

y^{^{''}} + 2 y^{^{'}} + y = sin (x) + 6 cos (2 x)

x \to - 2 lim (x^{3} + 6 x^{2} - 16)