Solve 4/3x^3*(-3x^3)=

$$\frac { 4 } { 3 } x ^ { 3 } \cdot ( - 3 x ^ { 3 } ) =$$

Evaluate

$$-4x^{6}$$

Solution Steps

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

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

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

$$-4x^{6}$$

Differentiate w.r.t. x

$$-24x^{5}$$

Steps Using Definition of a Derivative

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4x^{6})$$

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

$$6\left(-4\right)x^{6-1}$$

Multiply 6 times -4.

$$-24x^{6-1}$$

Subtract 1 from 6.

$$-24x^{5}$$