Solve (-1/2)^2x(-1/2)

$$( - \frac { 1 } { 2 } ) ^ { 2 } x ( - \frac { 1 } { 2 } )$$

Evaluate

$$-\frac{x}{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\left(-\frac{1}{2}\right)^{3}x$$

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$-\frac{1}{8}x$$

Differentiate w.r.t. x

$$-\frac{1}{8} = -0.125$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{1}{2}\right)^{3}x)$$

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

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

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

$$-\frac{1}{8}x^{1-1}$$

Subtract 1 from 1.

$$-\frac{1}{8}x^{0}$$

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

$$-\frac{1}{8}$$