Question

What is the derivative of this function?

Answer 1

$\bf y=\sqrt{x}-\left( \frac{1}{2} \right)^x\implies y=x^{\frac{1}{2}}-\left( \frac{1}{2} \right)^x\implies \cfrac{dy}{dx}=\frac{1}{2}x^{\frac{1}{2}-1}-\left( \frac{1}{2} \right)^xln\left( \frac{1}{2} \right) \\\\\\ \cfrac{dy}{dx}=\frac{1}{2}x^{-\frac{1}{2}}-\left( \frac{1}{2} \right)^xln\left( \frac{1}{2} \right)\implies \cfrac{dy}{dx}=\cfrac{1}{2\sqrt{x}}-\left( \frac{1}{2} \right)^xln\left( \frac{1}{2} \right)$