Solve (4x)(-3x^8)(-7x^3)

$$( 4 x ) ( - 3 x ^ { 8 } ) ( - 7 x ^ { 3 } )$$

Evaluate

$$84x^{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 8 to get 9.

$$4x^{9}\left(-3\right)\left(-7\right)x^{3}$$

To multiply powers of the same base, add their exponents. Add 9 and 3 to get 12.

$$4x^{12}\left(-3\right)\left(-7\right)$$

Multiply 4 and -3 to get -12.

$$-12x^{12}\left(-7\right)$$

Multiply -12 and -7 to get 84.

$$84x^{12}$$

Differentiate w.r.t. x

$$1008x^{11}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 8 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{9}\left(-3\right)\left(-7\right)x^{3})$$

To multiply powers of the same base, add their exponents. Add 9 and 3 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{12}\left(-3\right)\left(-7\right))$$

Multiply 4 and -3 to get -12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-12x^{12}\left(-7\right))$$

Multiply -12 and -7 to get 84.

$$\frac{\mathrm{d}}{\mathrm{d}x}(84x^{12})$$

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

$$12\times 84x^{12-1}$$

Multiply 12 times 84.

$$1008x^{12-1}$$

Subtract 1 from 12.

$$1008x^{11}$$