Solve dx/dx=2sqrt{x}dx

$$\frac { d x } { d x } = 2 \sqrt { x } d x$$

Solve for d

$$d=\frac{1}{2x^{\frac{3}{2}}}$$

$$x>0$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$2\sqrt{x}dx=\frac{\mathrm{d}(x)}{\mathrm{d}x}$$

The equation is in standard form.

$$2\sqrt{x}xd=1$$

Divide both sides by 2\sqrt{x}x.

$$\frac{2\sqrt{x}xd}{2\sqrt{x}x}=\frac{1}{2\sqrt{x}x}$$

Dividing by 2\sqrt{x}x undoes the multiplication by 2\sqrt{x}x.

$$d=\frac{1}{2\sqrt{x}x}$$

Divide 1 by 2\sqrt{x}x.

$$d=\frac{1}{2x^{\frac{3}{2}}}$$

Solve for x

$$x=\frac{\left(\frac{4}{d}\right)^{\frac{2}{3}}}{4}$$

$$d>0$$