derivative of (3x^{1/2})

解答

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

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

求解步骤

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

化简

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

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用幂法则:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 3^{\frac{1}{2}} \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

化简

3^{\frac{1}{2}} \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{3 ^{\frac{1}{2}}}{2 x ^{\frac{1}{2}}}

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

\frac{d}{d x} (14 e^{2 x})

(cos (6 x)) y^{^{'}} - 6 (tan (6 x)) y = - 2 sec (6 x)

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d er i v a t i v e x sin (x)

x \to 1 + lim (\frac{1}{x ^{3} - x ^{2}})