Solve -3x^3*1/9x^2

$$- 3 x ^ { 3 } \times \frac { 1 } { 9 } x ^ { 2 }$$

Evaluate

$$-\frac{x^{5}}{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-3x^{5}\times \frac{1}{9}$$

Multiply -3 and \frac{1}{9} to get -\frac{1}{3}.

$$-\frac{1}{3}x^{5}$$

Differentiate w.r.t. x

$$-\frac{5x^{4}}{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{5}\times \frac{1}{9})$$

Multiply -3 and \frac{1}{9} to get -\frac{1}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{1}{3}x^{5})$$

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

$$5\left(-\frac{1}{3}\right)x^{5-1}$$

Multiply 5 times -\frac{1}{3}.

$$-\frac{5}{3}x^{5-1}$$

Subtract 1 from 5.

$$-\frac{5}{3}x^{4}$$