Solve 2x^2*-x^2

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

Evaluate

$$-2x^{4}$$

Solution Steps

Multiply 2 and -1 to get -2.

$$-2x^{2}x^{2}$$

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

$$-2x^{4}$$

Differentiate w.r.t. x

$$-8x^{3}$$

Steps Using Definition of a Derivative

Multiply 2 and -1 to get -2.

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

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

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

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

$$4\left(-2\right)x^{4-1}$$

Multiply 4 times -2.

$$-8x^{4-1}$$

Subtract 1 from 4.

$$-8x^{3}$$