Solve (7x^4)(-3x^2)=

$$( 7 x ^ { 4 } ) ( - 3 x ^ { 2 } ) =$$

Evaluate

$$-21x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$7x^{6}\left(-3\right)$$

Multiply 7 and -3 to get -21.

$$-21x^{6}$$

Differentiate w.r.t. x

$$-126x^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{6}\left(-3\right))$$

Multiply 7 and -3 to get -21.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-21x^{6})$$

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

$$6\left(-21\right)x^{6-1}$$

Multiply 6 times -21.

$$-126x^{6-1}$$

Subtract 1 from 6.

$$-126x^{5}$$