derivative of cos(xln(x^2+1)-ln(x^4+1))

解答

\frac{d}{d x} (cos (x) ln (x^{2} + 1) - ln (x^{4} + 1))

- sin (x) ln (x^{2} + 1) + \frac{2 x cos ( x )}{x ^{2} + 1} - \frac{4 x ^{3}}{x ^{4} + 1}

求解步骤

\frac{d}{d x} (cos (x) ln (x^{2} + 1) - ln (x^{4} + 1))

使用微分加减法定则:

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

= \frac{d}{d x} (cos (x) ln (x^{2} + 1)) - \frac{d}{d x} (ln (x^{4} + 1))

\frac{d}{d x} (cos (x) ln (x^{2} + 1)) = - sin (x) ln (x^{2} + 1) + \frac{2 x cos ( x )}{x ^{2} + 1}

\frac{d}{d x} (ln (x^{4} + 1)) = \frac{4 x ^{3}}{x ^{4} + 1}

= - sin (x) ln (x^{2} + 1) + \frac{2 x cos ( x )}{x ^{2} + 1} - \frac{4 x ^{3}}{x ^{4} + 1}

y^{^{'}} = - y^{3}, y (0) = a

\frac{d}{d x} (\frac{e ^{x}}{9 x ^{2}})

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

n = 0 \sum \infty \frac{( - 1 ) ^{n + 1} ( x - 1 ) ^{n + 1}}{n + 1}

t an g e n t \frac{sin ( t )}{4 + 4 cos ( t )}