Solve 1.25*10^-3r

$$1.25 \times 10 ^ { - 3 } r$$

Evaluate

$$\frac{r}{800}$$

Solution Steps

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$1.25\times \frac{1}{1000}r$$

Multiply 1.25 and \frac{1}{1000} to get \frac{1}{800}.

$$\frac{1}{800}r$$

Differentiate w.r.t. r

$$0.00125$$

Steps Using Definition of a Derivative

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{\mathrm{d}}{\mathrm{d}r}(1.25\times \frac{1}{1000}r)$$

Multiply 1.25 and \frac{1}{1000} to get \frac{1}{800}.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{1}{800}r)$$

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

$$\frac{1}{800}r^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{800}r^{0}$$

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

$$\frac{1}{800}\times 1$$

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

$$\frac{1}{800}$$