Question

Differentiate: x√(x+4)

Answer 1

`\bf y=x√(x+4)\implies y=x\left( x+4 \right)^{(1)/(2)} \\\\\\ \cfrac{dy}{dx}=1\cdot \left( x+4 \right)^{(1)/(2)}~~+~~x\cdot \cfrac{1}{2}\left( x+4 \right)^{-(1)/(2)}\implies \cfrac{dy}{dx}=√(x+4)+\cfrac{x}{2√(x+4)} \\\\\\ \cfrac{dy}{dx}=\cfrac{2(x+4)~~+~~x}{2√(x+4)}\implies \cfrac{dy}{dx}=\cfrac{2x+8+x}{2√(x+4)}\implies \cfrac{dy}{dx}=\cfrac{3x+8}{2√(x+4)}`