derivative of (x^4+1^{1/2})

解答

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

\frac{2 x ^{3}}{( x ^{4} + 1 ) ^{\frac{1}{2}}}

求解步骤

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

使用连锁律:

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

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

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

= \frac{1}{2 ( x ^{4} + 1 ) ^{\frac{1}{2}}} \cdot 4 x^{3}

化简

\frac{1}{2 ( x ^{4} + 1 ) ^{\frac{1}{2}}} \cdot 4 x^{3} : \frac{2 x ^{3}}{( x ^{4} + 1 ) ^{\frac{1}{2}}}

= \frac{2 x ^{3}}{( x ^{4} + 1 ) ^{\frac{1}{2}}}

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

\frac{\partial}{\partial x} (4 sin (x))

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

d er i v a t i v e F (x) = 7 x^{6} (x^{4} - 7 x)

\frac{d}{d x} (tan (3 x))