Solve -2^2X(-2)^2

$$- 2 ^ { 2 } X ( - 2 ) ^ { 2 }$$

Evaluate

$$-16X$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$-4X\left(-2\right)^{2}$$

Calculate -2 to the power of 2 and get 4.

$$-4X\times 4$$

Multiply -4 and 4 to get -16.

$$-16X$$

Differentiate w.r.t. X

$$-16$$

Steps Using Definition of a Derivative

Calculate 2 to the power of 2 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}X}(-4X\left(-2\right)^{2})$$

Calculate -2 to the power of 2 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}X}(-4X\times 4)$$

Multiply -4 and 4 to get -16.

$$\frac{\mathrm{d}}{\mathrm{d}X}(-16X)$$

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

$$-16X^{1-1}$$

Subtract 1 from 1.

$$-16X^{0}$$

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

$$-16$$