Solve 2x^2*-3x^2

$$2 { x }^{ 2 } \times -3 { x }^{ 2 }$$

Evaluate

$$-6x^{4}$$

Solution Steps

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

$$2x^{4}\left(-3\right)$$

Multiply 2 and -3 to get -6.

$$-6x^{4}$$

Differentiate w.r.t. x

$$-24x^{3}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{4}\left(-3\right))$$

Multiply 2 and -3 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x^{4})$$

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

$$4\left(-6\right)x^{4-1}$$

Multiply 4 times -6.

$$-24x^{4-1}$$

Subtract 1 from 4.

$$-24x^{3}$$