Solve f(x)/dx=x^2

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

Solve for d

$$d=\frac{f}{x^{2}}$$

$$f\neq 0\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by dx.

$$fx=dxx^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$fx=dx^{3}$$

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

$$dx^{3}=fx$$

The equation is in standard form.

$$x^{3}d=fx$$

Divide both sides by x^{3}.

$$\frac{x^{3}d}{x^{3}}=\frac{fx}{x^{3}}$$

Dividing by x^{3} undoes the multiplication by x^{3}.

$$d=\frac{fx}{x^{3}}$$

Divide fx by x^{3}.

$$d=\frac{f}{x^{2}}$$

Variable d cannot be equal to 0.

$$d=\frac{f}{x^{2}}\text{, }d\neq 0$$

Solve for f

$$f=dx^{2}$$

$$d\neq 0\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by dx.

$$fx=dxx^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$fx=dx^{3}$$

The equation is in standard form.

$$xf=dx^{3}$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{dx^{3}}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{dx^{3}}{x}$$

Divide dx^{3} by x.

$$f=dx^{2}$$