Solve 8*10^-4a

$$8 \times 10 ^ { - 4 } a$$

Evaluate

$$\frac{a}{1250}$$

Solution Steps

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$8\times \frac{1}{10000}a$$

Multiply 8 and \frac{1}{10000} to get \frac{1}{1250}.

$$\frac{1}{1250}a$$

Differentiate w.r.t. a

$$\frac{1}{1250} = 0.0008$$

Steps Using Definition of a Derivative

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(8\times \frac{1}{10000}a)$$

Multiply 8 and \frac{1}{10000} to get \frac{1}{1250}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{1250}a)$$

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

$$\frac{1}{1250}a^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{1250}a^{0}$$

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

$$\frac{1}{1250}\times 1$$

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

$$\frac{1}{1250}$$