Solve 40%text{of}30p=

$$40 \% \text { of } 30 p =$$

Evaluate

$$12p$$

Solution Steps

Reduce the fraction \frac{40}{100} to lowest terms by extracting and canceling out 20.

$$\frac{2}{5}\times 30p$$

Express \frac{2}{5}\times 30 as a single fraction.

$$\frac{2\times 30}{5}p$$

Multiply 2 and 30 to get 60.

$$\frac{60}{5}p$$

Divide 60 by 5 to get 12.

$$12p$$

Differentiate w.r.t. p

$$12$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{40}{100} to lowest terms by extracting and canceling out 20.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{2}{5}\times 30p)$$

Express \frac{2}{5}\times 30 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{2\times 30}{5}p)$$

Multiply 2 and 30 to get 60.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{60}{5}p)$$

Divide 60 by 5 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}p}(12p)$$

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

$$12p^{1-1}$$

Subtract 1 from 1.

$$12p^{0}$$

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

$$12\times 1$$

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

$$12$$