Solve 30/40x%100

$$\frac{ 30 }{ 40 } x \% 100$$

Evaluate

$$\frac{3x}{4}$$

Solution Steps

Reduce the fraction \frac{30}{40} to lowest terms by extracting and canceling out 10.

$$\frac{3}{4}\times \frac{x}{100}\times 100$$

Express \frac{3}{4}\times 100 as a single fraction.

$$\frac{3\times 100}{4}\times \frac{x}{100}$$

Multiply 3 and 100 to get 300.

$$\frac{300}{4}\times \frac{x}{100}$$

Divide 300 by 4 to get 75.

$$75\times \frac{x}{100}$$

Express 75\times \frac{x}{100} as a single fraction.

$$\frac{75x}{100}$$

Divide 75x by 100 to get \frac{3}{4}x.

$$\frac{3}{4}x$$

Differentiate w.r.t. x

$$\frac{3}{4} = 0.75$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{30}{40} to lowest terms by extracting and canceling out 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{4}\times \frac{x}{100}\times 100)$$

Express \frac{3}{4}\times 100 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\times 100}{4}\times \frac{x}{100})$$

Multiply 3 and 100 to get 300.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{300}{4}\times \frac{x}{100})$$

Divide 300 by 4 to get 75.

$$\frac{\mathrm{d}}{\mathrm{d}x}(75\times \frac{x}{100})$$

Express 75\times \frac{x}{100} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{75x}{100})$$

Divide 75x by 100 to get \frac{3}{4}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{4}x)$$

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

$$\frac{3}{4}x^{1-1}$$

Subtract 1 from 1.

$$\frac{3}{4}x^{0}$$

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

$$\frac{3}{4}\times 1$$

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

$$\frac{3}{4}$$