Solve (-5x)*(3/5x^2)=

$$( - 5 x ) \cdot ( \frac { 3 } { 5 } x ^ { 2 } ) =$$

Evaluate

$$-3x^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

Multiply -5 and \frac{3}{5} to get -3.

$$-3x^{3}$$

Differentiate w.r.t. x

$$-9x^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

Multiply -5 and \frac{3}{5} to get -3.

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

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

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

Multiply 3 times -3.

$$-9x^{3-1}$$

Subtract 1 from 3.

$$-9x^{2}$$