Solve 2x(-3x^3x)

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

Evaluate

$$-6x^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$2x^{4}\left(-3\right)x$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$2x^{5}\left(-3\right)$$

Multiply 2 and -3 to get -6.

$$-6x^{5}$$

Differentiate w.r.t. x

$$-30x^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{4}\left(-3\right)x)$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{5}\left(-3\right))$$

Multiply 2 and -3 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x^{5})$$

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

$$5\left(-6\right)x^{5-1}$$

Multiply 5 times -6.

$$-30x^{5-1}$$

Subtract 1 from 5.

$$-30x^{4}$$