Solve (-3x)(-12x^2)

$$( - 3 x ) ( - 12 x ^ { 2 } )$$

Evaluate

$$36x^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

Multiply -3 and -12 to get 36.

$$36x^{3}$$

Differentiate w.r.t. x

$$108x^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

Multiply -3 and -12 to get 36.

$$\frac{\mathrm{d}}{\mathrm{d}x}(36x^{3})$$

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

$$3\times 36x^{3-1}$$

Multiply 3 times 36.

$$108x^{3-1}$$

Subtract 1 from 3.

$$108x^{2}$$