Derivative of Natural Logarithm Function/Examples/(x-2)^1/3 times (x-3)^1/2 times (2x-1)^3/2/Mistake

Source Work

1953: L. Harwood Clarke: A Note Book in Pure Mathematics:

$\text {II}$. Calculus: Differentiation: Variable Index: Example

Mistake

Let $y = \paren {x - 2}^{1/3} \paren {x - 3}^{1/2} \paren {2 x - 1}^{3/2}$,

then $\dfrac {\d y} {\d x} = \paren {\dfrac 1 {3 \paren {x - 2} } + \dfrac 1 {2 \paren {x - 3} } + \dfrac 3 {2 x - 1} } \paren {x - 1}^{1/3} \paren {x - 3}^{1/2} \paren {2 x - 1}^{3/2}$

Correction

Should be:

$\dfrac {\d y} {\d x} = \paren {\dfrac 1 {3 \paren {x - 2} } + \dfrac 1 {2 \paren {x - 3} } + \dfrac 3 {2 x - 1} } \paren {x - 2}^{1/3} \paren {x - 3}^{1/2} \paren {2 x - 1}^{3/2}$

See Derivative of $\paren {x - 2}^{1/3} \paren {x - 3}^{1/2} \paren {2 x - 1}^{3/2}$.

Sources

• 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text {II}$. Calculus: Differentiation: Variable Index: Example