Solve (2/3x^3)*(-6x)

$$( \frac { 2 } { 3 } x ^ { 3 } ) \cdot ( - 6 x )$$

Evaluate

$$-4x^{4}$$

Solution Steps

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

$$\frac{2}{3}x^{4}\left(-6\right)$$

Multiply \frac{2}{3} and -6 to get -4.

$$-4x^{4}$$

Differentiate w.r.t. x

$$-16x^{3}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{3}x^{4}\left(-6\right))$$

Multiply \frac{2}{3} and -6 to get -4.

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

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

$$4\left(-4\right)x^{4-1}$$

Multiply 4 times -4.

$$-16x^{4-1}$$

Subtract 1 from 4.

$$-16x^{3}$$