Solve -8*3x-x/2

$$- 8 \cdot 3 x - \frac { x } { 2 }$$

Evaluate

$$-\frac{49x}{2}$$

Solution Steps

Multiply -8 and 3 to get -24.

$$-24x-\frac{x}{2}$$

Combine -24x and -\frac{x}{2} to get -\frac{49}{2}x.

$$-\frac{49}{2}x$$

Differentiate w.r.t. x

$$-\frac{49}{2} = -24\frac{1}{2} = -24.5$$

Steps Using Definition of a Derivative

Multiply -8 and 3 to get -24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-24x-\frac{x}{2})$$

Combine -24x and -\frac{x}{2} to get -\frac{49}{2}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{49}{2}x)$$

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

$$-\frac{49}{2}x^{1-1}$$

Subtract 1 from 1.

$$-\frac{49}{2}x^{0}$$

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

$$-\frac{49}{2}$$