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

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

Evaluate

$$-3x^{7}$$

Solution Steps

Multiply 3 and -1 to get -3.

$$-3x^{4}x^{3}$$

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

$$-3x^{7}$$

Differentiate w.r.t. x

$$-21x^{6}$$

Steps Using Definition of a Derivative

Multiply 3 and -1 to get -3.

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{7})$$

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

$$7\left(-3\right)x^{7-1}$$

Multiply 7 times -3.

$$-21x^{7-1}$$

Subtract 1 from 7.

$$-21x^{6}$$