Solve 8x10^-4

$$8 x 10 ^ { - 4 }$$

Evaluate

$$\frac{x}{1250}$$

Solution Steps

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

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

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

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

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

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

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

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

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

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

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

Subtract 1 from 1.

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

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.

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