Solve (6x^5)(-2x^2)

$$( 6 x ^ { 5 } ) ( - 2 x ^ { 2 } )$$

Evaluate

$$-12x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$6x^{7}\left(-2\right)$$

Multiply 6 and -2 to get -12.

$$-12x^{7}$$

Differentiate w.r.t. x

$$-84x^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{7}\left(-2\right))$$

Multiply 6 and -2 to get -12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-12x^{7})$$

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

$$7\left(-12\right)x^{7-1}$$

Multiply 7 times -12.

$$-84x^{7-1}$$

Subtract 1 from 7.

$$-84x^{6}$$