Solve 5,000*10%*24r

$$5,000 \times 10 \% \times 24 r$$

Evaluate

$$12000r$$

Solution Steps

Reduce the fraction \frac{10}{100} to lowest terms by extracting and canceling out 10.

$$5000\times \frac{1}{10}\times 24r$$

Multiply 5000 and \frac{1}{10} to get \frac{5000}{10}.

$$\frac{5000}{10}\times 24r$$

Divide 5000 by 10 to get 500.

$$500\times 24r$$

Multiply 500 and 24 to get 12000.

$$12000r$$

Differentiate w.r.t. r

$$12000$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{10}{100} to lowest terms by extracting and canceling out 10.

$$\frac{\mathrm{d}}{\mathrm{d}r}(5000\times \frac{1}{10}\times 24r)$$

Multiply 5000 and \frac{1}{10} to get \frac{5000}{10}.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{5000}{10}\times 24r)$$

Divide 5000 by 10 to get 500.

$$\frac{\mathrm{d}}{\mathrm{d}r}(500\times 24r)$$

Multiply 500 and 24 to get 12000.

$$\frac{\mathrm{d}}{\mathrm{d}r}(12000r)$$

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

$$12000r^{1-1}$$

Subtract 1 from 1.

$$12000r^{0}$$

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

$$12000\times 1$$

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

$$12000$$