Solve 48%text{of}55L

$$48 \% \text { of } 55 L$$

Evaluate

$$\frac{132L}{5}$$

Solution Steps

Reduce the fraction \frac{48}{100} to lowest terms by extracting and canceling out 4.

$$\frac{12}{25}\times 55L$$

Express \frac{12}{25}\times 55 as a single fraction.

$$\frac{12\times 55}{25}L$$

Multiply 12 and 55 to get 660.

$$\frac{660}{25}L$$

Reduce the fraction \frac{660}{25} to lowest terms by extracting and canceling out 5.

$$\frac{132}{5}L$$

Differentiate w.r.t. L

$$\frac{132}{5} = 26\frac{2}{5} = 26.4$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{48}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\mathrm{d}}{\mathrm{d}L}(\frac{12}{25}\times 55L)$$

Express \frac{12}{25}\times 55 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}L}(\frac{12\times 55}{25}L)$$

Multiply 12 and 55 to get 660.

$$\frac{\mathrm{d}}{\mathrm{d}L}(\frac{660}{25}L)$$

Reduce the fraction \frac{660}{25} to lowest terms by extracting and canceling out 5.

$$\frac{\mathrm{d}}{\mathrm{d}L}(\frac{132}{5}L)$$

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

$$\frac{132}{5}L^{1-1}$$

Subtract 1 from 1.

$$\frac{132}{5}L^{0}$$

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

$$\frac{132}{5}\times 1$$

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

$$\frac{132}{5}$$