derivative of 1/pi cx^2+ln(cos^3(x))

解答

\frac{d}{d x} (\frac{1}{π} c x^{2} + ln (cos^{3} (x)))

\frac{2 c x}{π} - 3 tan (x)

求解步骤

\frac{d}{d x} (\frac{1}{π} c x^{2} + ln (cos^{3} (x)))

化简

\frac{1}{π} c x^{2} + ln (cos^{3} (x)) : \frac{c x ^{2}}{π} + ln (cos^{3} (x))

= \frac{d}{d x} (\frac{c x ^{2}}{π} + ln (cos^{3} (x)))

使用微分加减法定则:

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

= \frac{d}{d x} (\frac{c x ^{2}}{π}) + \frac{d}{d x} (ln (cos^{3} (x)))

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

\frac{d}{d x} (ln (cos^{3} (x))) = - 3 tan (x)

= \frac{2 c x}{π} - 3 tan (x)

\int_{1}^{9} \frac{1}{6 - x} d x

a re a 3 x, (x - 1)^{2}

\int \frac{1}{x} 1 + x^{2} d x

t an g e n t f (x) = x^{3} - 2 x + 2, (2, 6)

4 t \frac{d y}{d t} - 3 y = t