Solve (4x^2)(-7x^5)(8x^4)

$$( 4 x ^ { 2 } ) ( - 7 x ^ { 5 } ) ( 8 x ^ { 4 } )$$

Evaluate

$$-224x^{11}$$

Solution Steps

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

$$4x^{7}\left(-7\right)\times 8x^{4}$$

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

$$4x^{11}\left(-7\right)\times 8$$

Multiply 4 and -7 to get -28.

$$-28x^{11}\times 8$$

Multiply -28 and 8 to get -224.

$$-224x^{11}$$

Differentiate w.r.t. x

$$-2464x^{10}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{7}\left(-7\right)\times 8x^{4})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{11}\left(-7\right)\times 8)$$

Multiply 4 and -7 to get -28.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-28x^{11}\times 8)$$

Multiply -28 and 8 to get -224.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-224x^{11})$$

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

$$11\left(-224\right)x^{11-1}$$

Multiply 11 times -224.

$$-2464x^{11-1}$$

Subtract 1 from 11.

$$-2464x^{10}$$