Differentiate the following with respect to $x$, leaving your answers in term of $x$. ${{e}^{ex}}\co

Question

Differentiate the following with respect to $x$, leaving your answers in term of $x$. ${{e}^{ex}}\cot \left( \frac{x}{2} \right)$ [3] ${{\left( 2x \right)}^{1/x}}$ [4]

Accepted Answer

(a) $e^{ex}\left[e\cot\left(\frac x2\right)-\frac12\csc^2\left(\frac x2\right)\right]$ (b) $\frac{(2x)^{1/x}}{x^2}[1-\ln(2x)]$

2010 ACJC Promo Q5

2010 ACJC Promo Q5

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