derivative (sin(q)+cos(q))/(cos(q))

解答

导数

\frac{sin ( q ) + cos ( q )}{cos ( q )}

sec^{2} (q)

求解步骤

\frac{d}{d q} (\frac{sin ( q ) + cos ( q )}{cos ( q )})

化简

\frac{sin ( q ) + cos ( q )}{cos ( q )} : 1 + tan (q)

= \frac{d}{d q} (1 + tan (q))

使用微分加减法定则:

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

= \frac{d}{d q} (1) + \frac{d}{d q} (tan (q))

\frac{d}{d q} (1) = 0

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

= 0 + sec^{2} (q)

化简

= sec^{2} (q)

in v erse l a pl a ce \frac{4}{s ( s ^{2} + 2 s + 4 )}

x \to - 8 lim (3 x + 1)

\frac{d}{d x} (cos^{2} (x) + 1)

x \to 5 lim (\frac{x + 2}{x ^{2} - 5})

\frac{d}{d x} (2 - cosh (x - 1))