Solve 2x^2*(-2x^2)

$$2 { x }^{ 2 } \times (-2 { x }^{ 2 } )$$

Evaluate

$$-4x^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

Multiply 2 and -2 to get -4.

$$-4x^{4}$$

Differentiate w.r.t. x

$$-16x^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

Multiply 2 and -2 to get -4.

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

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

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

Multiply 4 times -4.

$$-16x^{4-1}$$

Subtract 1 from 4.

$$-16x^{3}$$