Solve (-8)(7x)(1/2)

$$( - 8 ) ( 7 x ) ( \frac { 1 } { 2 } )$$

Evaluate

$$-28x$$

Solution Steps

Multiply -8 and 7 to get -56.

$$-56x\times \frac{1}{2}$$

Multiply -56 and \frac{1}{2} to get \frac{-56}{2}.

$$\frac{-56}{2}x$$

Divide -56 by 2 to get -28.

$$-28x$$

Differentiate w.r.t. x

$$-28$$

Steps Using Definition of a Derivative

Multiply -8 and 7 to get -56.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-56x\times \frac{1}{2})$$

Multiply -56 and \frac{1}{2} to get \frac{-56}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-56}{2}x)$$

Divide -56 by 2 to get -28.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-28x)$$

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

$$-28x^{1-1}$$

Subtract 1 from 1.

$$-28x^{0}$$

For any term t except 0, t^{0}=1.

$$-28$$