Solve (-2x)(-1.5x)(-7)=

$$(-2x)(-1.5x)(-7)=$$

Evaluate

$$-21x^{2}$$

Solution Steps

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

$$-2x^{2}\left(-1.5\right)\left(-7\right)$$

Multiply -2 and -1.5 to get 3.

$$3x^{2}\left(-7\right)$$

Multiply 3 and -7 to get -21.

$$-21x^{2}$$

Differentiate w.r.t. x

$$-42x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{2}\left(-1.5\right)\left(-7\right))$$

Multiply -2 and -1.5 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}\left(-7\right))$$

Multiply 3 and -7 to get -21.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-21x^{2})$$

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

$$2\left(-21\right)x^{2-1}$$

Multiply 2 times -21.

$$-42x^{2-1}$$

Subtract 1 from 2.

$$-42x^{1}$$

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

$$-42x$$