Solve f(x)^prime=2/2x+1

$$f ( x ) ^ { \prime } = \frac { 2 } { 2 x + 1 }$$

Solve for f

$$f=\frac{2}{2x+1}$$

$$x\neq -\frac{1}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x+1.

$$f\frac{\mathrm{d}}{\mathrm{d}x}(x)\left(2x+1\right)=2$$

Use the distributive property to multiply f\frac{\mathrm{d}}{\mathrm{d}x}(x) by 2x+1.

$$2f\frac{\mathrm{d}}{\mathrm{d}x}(x)x+f\frac{\mathrm{d}}{\mathrm{d}x}(x)=2$$

Combine all terms containing f.

$$\left(2\frac{\mathrm{d}}{\mathrm{d}x}(x)x+\frac{\mathrm{d}}{\mathrm{d}x}(x)\right)f=2$$

The equation is in standard form.

$$\left(2x+1\right)f=2$$

Divide both sides by 2x+1.

$$\frac{\left(2x+1\right)f}{2x+1}=\frac{2}{2x+1}$$

Dividing by 2x+1 undoes the multiplication by 2x+1.

$$f=\frac{2}{2x+1}$$

Solve for x

$$x=-\frac{1}{2}+\frac{1}{f}$$

$$f\neq 0$$