Solve 3x(-6x^5)

$$3 x ( - 6 x ^ { 5 } )$$

Evaluate

$$-18x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$3x^{6}\left(-6\right)$$

Multiply 3 and -6 to get -18.

$$-18x^{6}$$

Differentiate w.r.t. x

$$-108x^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{6}\left(-6\right))$$

Multiply 3 and -6 to get -18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-18x^{6})$$

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

$$6\left(-18\right)x^{6-1}$$

Multiply 6 times -18.

$$-108x^{6-1}$$

Subtract 1 from 6.

$$-108x^{5}$$