Question

What is the derivative of this function?

Answer 1

`\bf y=√(x)-\left( (1)/(2) \right)^x\implies y=x^{(1)/(2)}-\left( (1)/(2) \right)^x\implies \cfrac{dy}{dx}=(1)/(2)x^{(1)/(2)-1}-\left( (1)/(2) \right)^xln\left( (1)/(2) \right) \\\\\\ \cfrac{dy}{dx}=(1)/(2)x^{-(1)/(2)}-\left( (1)/(2) \right)^xln\left( (1)/(2) \right)\implies \cfrac{dy}{dx}=\cfrac{1}{2√(x)}-\left( (1)/(2) \right)^xln\left( (1)/(2) \right)`