Solve (-4.7x^4)(6x^7)

$$( - 4.7 x ^ { 4 } ) ( 6 x ^ { 7 } )$$

Evaluate

$$-\frac{141x^{11}}{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

$$-4.7x^{11}\times 6$$

Multiply -4.7 and 6 to get -28.2.

$$-28.2x^{11}$$

Differentiate w.r.t. x

$$-\frac{1551x^{10}}{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4.7x^{11}\times 6)$$

Multiply -4.7 and 6 to get -28.2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-28.2x^{11})$$

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

$$11\left(-28.2\right)x^{11-1}$$

Multiply 11 times -28.2.

$$-310.2x^{11-1}$$

Subtract 1 from 11.

$$-310.2x^{10}$$