derivative f(x)=e^{sqrt(x^3+1)}

解答

导数

f (x) = e^{x^{3} + 1}

\frac{3 e ^{x^{3} + 1} x ^{2}}{2 x ^{3} + 1}

求解步骤

\frac{d}{d x} (e^{x^{3} + 1})

使用连锁律:

e^{x^{3} + 1} \frac{d}{d x} (x^{3} + 1)

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

\frac{d}{d x} (x^{3} + 1) = \frac{3 x ^{2}}{2 x ^{3} + 1}

= e^{x^{3} + 1} \frac{3 x ^{2}}{2 x ^{3} + 1}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 e ^{x^{3} + 1} x ^{2}}{2 x ^{3} + 1}

d er i v a t i v e f (x) = 3 x^{5}

d er i v a t i v e y = \frac{1}{2 x - 1}

d er i v a t i v e f (x) = \frac{x ^{3} + 5}{x ^{2} + 1}

\frac{d}{d x} (arccos (2 x^{2}))

\int 2 + t^{2} d t