Solve 5x^3*-2x^3

$$5 { x }^{ 3 } \times -2 { x }^{ 3 }$$

Evaluate

$$-10x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$5x^{6}\left(-2\right)$$

Multiply 5 and -2 to get -10.

$$-10x^{6}$$

Differentiate w.r.t. x

$$-60x^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{6}\left(-2\right))$$

Multiply 5 and -2 to get -10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-10x^{6})$$

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

$$6\left(-10\right)x^{6-1}$$

Multiply 6 times -10.

$$-60x^{6-1}$$

Subtract 1 from 6.

$$-60x^{5}$$