Solve x^2-4x^2/5

$$x ^ { 2 } - \frac { 4 x ^ { 2 } } { 5 }$$

Evaluate

$$\frac{x^{2}}{5}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2} times \frac{5}{5}.

$$\frac{5x^{2}}{5}-\frac{4x^{2}}{5}$$

Since \frac{5x^{2}}{5} and \frac{4x^{2}}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5x^{2}-4x^{2}}{5}$$

Combine like terms in 5x^{2}-4x^{2}.

$$\frac{x^{2}}{5}$$

Differentiate w.r.t. x

$$\frac{2x}{5}$$

Steps Using Definition of a Derivative

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2} times \frac{5}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x^{2}}{5}-\frac{4x^{2}}{5})$$

Since \frac{5x^{2}}{5} and \frac{4x^{2}}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x^{2}-4x^{2}}{5})$$

Combine like terms in 5x^{2}-4x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}}{5})$$

The derivative of ax^{n} is nax^{n-1}.

$$2\times \frac{1}{5}x^{2-1}$$

Multiply 2 times \frac{1}{5}.

$$\frac{2}{5}x^{2-1}$$

Subtract 1 from 2.

$$\frac{2}{5}x^{1}$$

For any term t, t^{1}=t.

$$\frac{2}{5}x$$