Solve 10r*15*54=

$$10 r \cdot 15 \cdot 5 4 =$$

Evaluate

$$3000r$$

Solution Steps

Multiply 10 and 15 to get 150.

$$150r\times 5\times 4$$

Multiply 150 and 5 to get 750.

$$750r\times 4$$

Multiply 750 and 4 to get 3000.

$$3000r$$

Differentiate w.r.t. r

$$3000$$

Steps Using Definition of a Derivative

Multiply 10 and 15 to get 150.

$$\frac{\mathrm{d}}{\mathrm{d}r}(150r\times 5\times 4)$$

Multiply 150 and 5 to get 750.

$$\frac{\mathrm{d}}{\mathrm{d}r}(750r\times 4)$$

Multiply 750 and 4 to get 3000.

$$\frac{\mathrm{d}}{\mathrm{d}r}(3000r)$$

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

$$3000r^{1-1}$$

Subtract 1 from 1.

$$3000r^{0}$$

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

$$3000\times 1$$

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

$$3000$$