Solve (5x)(-3x)

$$( 5 x ) ( - 3 x )$$

Evaluate

$$-15x^{2}$$

Solution Steps

Multiply x and x to get x^{2}.

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

Multiply 5 and -3 to get -15.

$$-15x^{2}$$

Differentiate w.r.t. x

$$-30x$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

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

Multiply 5 and -3 to get -15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-15x^{2})$$

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

$$2\left(-15\right)x^{2-1}$$

Multiply 2 times -15.

$$-30x^{2-1}$$

Subtract 1 from 2.

$$-30x^{1}$$

For any term t, t^{1}=t.

$$-30x$$