2 ___ x *\/ x
d / 2 ___\ --\x *\/ x / dx
Apply the product rule:
f(x)=x2f{\left(x \right)} = x^{2}f(x)=x2; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}dxdf(x):
Apply the power rule: x2x^{2}x2 goes to 2x2 x2x
g(x)=xg{\left(x \right)} = \sqrt{x}g(x)=x; to find ddxg(x)\frac{d}{d x} g{\left(x \right)}dxdg(x):
Apply the power rule: x\sqrt{x}x goes to 12x\frac{1}{2 \sqrt{x}}2x1
The result is: 5x322\frac{5 x^{\frac{3}{2}}}{2}25x23
The answer is:
3/2 5*x ------ 2
___ 15*\/ x -------- 4
15 ------- ___ 8*\/ x