Solve x/25-3x/80

$$\frac { x } { 25 } - \frac { 3 x } { 80 }$$

Evaluate

$$\frac{x}{400}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25 and 80 is 400. Multiply \frac{x}{25} times \frac{16}{16}. Multiply \frac{3x}{80} times \frac{5}{5}.

$$\frac{16x}{400}-\frac{5\times 3x}{400}$$

Since \frac{16x}{400} and \frac{5\times 3x}{400} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16x-5\times 3x}{400}$$

Do the multiplications in 16x-5\times 3x.

$$\frac{16x-15x}{400}$$

Combine like terms in 16x-15x.

$$\frac{x}{400}$$

Differentiate w.r.t. x

$$\frac{1}{400} = 0.0025$$

Steps Using Definition of a Derivative

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25 and 80 is 400. Multiply \frac{x}{25} times \frac{16}{16}. Multiply \frac{3x}{80} times \frac{5}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16x}{400}-\frac{5\times 3x}{400})$$

Since \frac{16x}{400} and \frac{5\times 3x}{400} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16x-5\times 3x}{400})$$

Do the multiplications in 16x-5\times 3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16x-15x}{400})$$

Combine like terms in 16x-15x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{400})$$

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

$$\frac{1}{400}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{400}x^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{1}{400}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1}{400}$$