derivative (6x^2+11)^{1/2}

解答

导数

(6 x^{2} + 11)^{\frac{1}{2}}

\frac{6 x}{( 6 x ^{2} + 11 ) ^{\frac{1}{2}}}

求解步骤

\frac{d}{d x} ((6 x^{2} + 11)^{\frac{1}{2}})

使用连锁律:

\frac{1}{2 ( 6 x ^{2} + 11 ) ^{\frac{1}{2}}} \frac{d}{d x} (6 x^{2} + 11)

= \frac{1}{2 ( 6 x ^{2} + 11 ) ^{\frac{1}{2}}} \frac{d}{d x} (6 x^{2} + 11)

\frac{d}{d x} (6 x^{2} + 11) = 12 x

= \frac{1}{2 ( 6 x ^{2} + 11 ) ^{\frac{1}{2}}} \cdot 12 x

化简

\frac{1}{2 ( 6 x ^{2} + 11 ) ^{\frac{1}{2}}} \cdot 12 x : \frac{6 x}{( 6 x ^{2} + 11 ) ^{\frac{1}{2}}}

= \frac{6 x}{( 6 x ^{2} + 11 ) ^{\frac{1}{2}}}

d er i v a t i v e 3 x^{2} - 1

d er i v a t i v e e^{2} x + 3

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

d er i v a t i v e f (x) = 4 + x

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