Solve 2*10^-12x

$$2 \times 10 ^ { - 12 } x$$

Evaluate

$$\frac{x}{500000000000}$$

Solution Steps

Calculate 10 to the power of -12 and get \frac{1}{1000000000000}.

$$2\times \frac{1}{1000000000000}x$$

Multiply 2 and \frac{1}{1000000000000} to get \frac{1}{500000000000}.

$$\frac{1}{500000000000}x$$

Differentiate w.r.t. x

$$\frac{1}{500000000000} = 2 \times 10^{-12}$$

Steps Using Definition of a Derivative

Calculate 10 to the power of -12 and get \frac{1}{1000000000000}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2\times \frac{1}{1000000000000}x)$$

Multiply 2 and \frac{1}{1000000000000} to get \frac{1}{500000000000}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{500000000000}x)$$

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

$$\frac{1}{500000000000}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{500000000000}x^{0}$$

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

$$\frac{1}{500000000000}\times 1$$

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

$$\frac{1}{500000000000}$$