derivative of-5cos(cos(x^6))

解答

\frac{d}{d x} (- 5 cos (cos (x^{6})))

- 30 x^{5} sin (cos (x^{6})) sin (x^{6})

求解步骤

\frac{d}{d x} (- 5 cos (cos (x^{6})))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= - 5 \frac{d}{d x} (cos (cos (x^{6})))

使用连锁律:

- sin (cos (x^{6})) \frac{d}{d x} (cos (x^{6}))

= - sin (cos (x^{6})) \frac{d}{d x} (cos (x^{6}))

\frac{d}{d x} (cos (x^{6})) = - sin (x^{6}) \cdot 6 x^{5}

= - 5 (- sin (cos (x^{6})) (- sin (x^{6}) \cdot 6 x^{5}))

化简

= - 30 x^{5} sin (cos (x^{6})) sin (x^{6})

x \to 0 lim (- \frac{1}{x})

\int \frac{48 x ^{2}}{x ^{4} - 74 x ^{2} + 1225} d x

in v erse l a pl a ce - \frac{1}{s}

x \to 0 lim (1 - x^{2})

x \to \frac{3 π}{2} lim (sec (x))