Solve 45x-2x-5x+2x

$$45 x - 2 x - 5 x + 2 x$$

Evaluate

$$40x$$

Solution Steps

Combine 45x and -2x to get 43x.

$$43x-5x+2x$$

Combine 43x and -5x to get 38x.

$$38x+2x$$

Combine 38x and 2x to get 40x.

$$40x$$

Differentiate w.r.t. x

$$40$$

Steps Using Definition of a Derivative

Combine 45x and -2x to get 43x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(43x-5x+2x)$$

Combine 43x and -5x to get 38x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(38x+2x)$$

Combine 38x and 2x to get 40x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(40x)$$

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

$$40x^{1-1}$$

Subtract 1 from 1.

$$40x^{0}$$

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

$$40\times 1$$

For any term t, t\times 1=t and 1t=t.

$$40$$