Solve (-6x^3)(7x^4)

$$( - 6 x ^ { 3 } ) ( 7 x ^ { 4 } )$$

Evaluate

$$-42x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-6x^{7}\times 7$$

Multiply -6 and 7 to get -42.

$$-42x^{7}$$

Differentiate w.r.t. x

$$-294x^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x^{7}\times 7)$$

Multiply -6 and 7 to get -42.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-42x^{7})$$

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

$$7\left(-42\right)x^{7-1}$$

Multiply 7 times -42.

$$-294x^{7-1}$$

Subtract 1 from 7.

$$-294x^{6}$$