Solve (75div100*90div100*x)

$$(75 \div 100 \times 90 \div 100 \times x)$$

Evaluate

$$\frac{27x}{40}$$

Solution Steps

Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{3}{4}\times 90}{100}x$$

Express \frac{3}{4}\times 90 as a single fraction.

$$\frac{\frac{3\times 90}{4}}{100}x$$

Multiply 3 and 90 to get 270.

$$\frac{\frac{270}{4}}{100}x$$

Reduce the fraction \frac{270}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{135}{2}}{100}x$$

Express \frac{\frac{135}{2}}{100} as a single fraction.

$$\frac{135}{2\times 100}x$$

Multiply 2 and 100 to get 200.

$$\frac{135}{200}x$$

Reduce the fraction \frac{135}{200} to lowest terms by extracting and canceling out 5.

$$\frac{27}{40}x$$

Differentiate w.r.t. x

$$\frac{27}{40} = 0.675$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{3}{4}\times 90}{100}x)$$

Express \frac{3}{4}\times 90 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{3\times 90}{4}}{100}x)$$

Multiply 3 and 90 to get 270.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{270}{4}}{100}x)$$

Reduce the fraction \frac{270}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{135}{2}}{100}x)$$

Express \frac{\frac{135}{2}}{100} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{135}{2\times 100}x)$$

Multiply 2 and 100 to get 200.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{135}{200}x)$$

Reduce the fraction \frac{135}{200} to lowest terms by extracting and canceling out 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{27}{40}x)$$

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

$$\frac{27}{40}x^{1-1}$$

Subtract 1 from 1.

$$\frac{27}{40}x^{0}$$

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

$$\frac{27}{40}\times 1$$

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

$$\frac{27}{40}$$