___ (x - 3)*\/ x
(x - 3)*sqrt(x)
Apply the product rule:
f(x)=x−3f{\left(x \right)} = x - 3f(x)=x−3; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}dxdf(x):
Differentiate x−3x - 3x−3 term by term:
Apply the power rule: xxx goes to 111
The derivative of the constant −3-3−3 is zero.
The result is: 111
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: x+x−32x\sqrt{x} + \frac{x - 3}{2 \sqrt{x}}x+2xx−3
Now simplify:
The answer is:
___ x - 3 \/ x + ------- ___ 2*\/ x
-3 + x 1 - ------ 4*x ---------- ___ \/ x
/ -3 + x\ 3*|-2 + ------| \ x / --------------- 3/2 8*x