Solve (-2x)(-15x)(-7)=

$$(-2x)(-15x)(-7)=$$

Evaluate

$$-210x^{2}$$

Solution Steps

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

$$-2x^{2}\left(-15\right)\left(-7\right)$$

Multiply -2 and -15 to get 30.

$$30x^{2}\left(-7\right)$$

Multiply 30 and -7 to get -210.

$$-210x^{2}$$

Differentiate w.r.t. x

$$-420x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{2}\left(-15\right)\left(-7\right))$$

Multiply -2 and -15 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}x}(30x^{2}\left(-7\right))$$

Multiply 30 and -7 to get -210.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-210x^{2})$$

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

$$2\left(-210\right)x^{2-1}$$

Multiply 2 times -210.

$$-420x^{2-1}$$

Subtract 1 from 2.

$$-420x^{1}$$

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

$$-420x$$