Solve 12x^-42x

$$12 { x }^{ } -42x$$

Evaluate

$$-30x$$

Solution Steps

Calculate x to the power of 1 and get x.

$$12x-42x$$

Combine 12x and -42x to get -30x.

$$-30x$$

Differentiate w.r.t. x

$$-30$$

Steps Using Definition of a Derivative

Calculate x to the power of 1 and get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x-42x)$$

Combine 12x and -42x to get -30x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-30x)$$

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

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

Subtract 1 from 1.

$$-30x^{0}$$

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

$$-30$$