Solve (-x)(-4)left(-x^2right)^

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

Evaluate

$$-4x^{3}$$

Solution Steps

Calculate -x^{2} to the power of 1 and get -x^{2}.

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

Multiply -4 and -1 to get 4.

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

Multiply -1 and 4 to get -4.

$$-4xx^{2}$$

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

$$-4x^{3}$$

Differentiate w.r.t. x

$$-12x^{2}$$

Steps Using Definition of a Derivative

Calculate -x^{2} to the power of 1 and get -x^{2}.

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

Multiply -4 and -1 to get 4.

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

Multiply -1 and 4 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4xx^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4x^{3})$$

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

$$3\left(-4\right)x^{3-1}$$

Multiply 3 times -4.

$$-12x^{3-1}$$

Subtract 1 from 3.

$$-12x^{2}$$