Solve (-3x^-3)(4x^6)

$$( - 3 x ^ { - 3 } ) ( 4 x ^ { 6 } )$$

Evaluate

$$-12x^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -3 and 6 to get 3.

$$-3x^{3}\times 4$$

Multiply -3 and 4 to get -12.

$$-12x^{3}$$

Differentiate w.r.t. x

$$-36x^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -3 and 6 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{3}\times 4)$$

Multiply -3 and 4 to get -12.

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

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

$$3\left(-12\right)x^{3-1}$$

Multiply 3 times -12.

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

Subtract 1 from 3.

$$-36x^{2}$$