derivative of log_{e}(sqrt(x^2+1))

解答

\frac{d}{d x} (lo g_{e} (x^{2} + 1))

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

求解步骤

\frac{d}{d x} (lo g_{e} (x^{2} + 1))

化简

lo g_{e} (x^{2} + 1) : ln (x^{2} + 1)

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

使用连锁律:

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

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

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

= \frac{1}{x ^{2} + 1} \cdot \frac{x}{x ^{2} + 1}

化简

\frac{1}{x ^{2} + 1} \cdot \frac{x}{x ^{2} + 1} : \frac{x}{x ^{2} + 1}

= \frac{x}{x ^{2} + 1}

d er i v a t i v e y = (tan (- 1 (3 x))) 2

d er i v a t i v e x x

d er i v a t i v e - 0.6 t^{2} + 30 t

\int_{0}^{5} π (- \frac{3}{5} x + 3)^{2} d x

d er i v a t i v e \frac{t ^{3} + 3 t}{t ^{2} - 4 t + 3}