Solve d/dxf(x)=f^prime(x)

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

Solve for f (complex solution)

$$f\in \mathrm{C}$$

Solution Steps

Subtract \frac{\mathrm{d}}{\mathrm{d}x}(f)x from both sides.

$$\frac{\mathrm{d}}{\mathrm{d}x}(f)x-\frac{\mathrm{d}}{\mathrm{d}x}(f)x=0$$

Combine \frac{\mathrm{d}}{\mathrm{d}x}(f)x and -\frac{\mathrm{d}}{\mathrm{d}x}(f)x to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any f.

$$f\in \mathrm{C}$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

Subtract \frac{\mathrm{d}}{\mathrm{d}x}(f)x from both sides.

$$\frac{\mathrm{d}}{\mathrm{d}x}(f)x-\frac{\mathrm{d}}{\mathrm{d}x}(f)x=0$$

Combine \frac{\mathrm{d}}{\mathrm{d}x}(f)x and -\frac{\mathrm{d}}{\mathrm{d}x}(f)x to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for f

$$f\in \mathrm{R}$$

Solution Steps

Subtract \frac{\mathrm{d}}{\mathrm{d}x}(f)x from both sides.

$$\frac{\mathrm{d}}{\mathrm{d}x}(f)x-\frac{\mathrm{d}}{\mathrm{d}x}(f)x=0$$

Combine \frac{\mathrm{d}}{\mathrm{d}x}(f)x and -\frac{\mathrm{d}}{\mathrm{d}x}(f)x to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any f.

$$f\in \mathrm{R}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Subtract \frac{\mathrm{d}}{\mathrm{d}x}(f)x from both sides.

$$\frac{\mathrm{d}}{\mathrm{d}x}(f)x-\frac{\mathrm{d}}{\mathrm{d}x}(f)x=0$$

Combine \frac{\mathrm{d}}{\mathrm{d}x}(f)x and -\frac{\mathrm{d}}{\mathrm{d}x}(f)x to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$