Solve x-4+2x+18.2+x+4+1x+25.5

$$x-4+2x+18.2+x+4+1x+25.5$$

Evaluate

$$5x+43.7$$

Solution Steps

Combine x and 2x to get 3x.

$$3x-4+18.2+x+4+1x+25.5$$

Add -4 and 18.2 to get 14.2.

$$3x+14.2+x+4+1x+25.5$$

Combine 3x and x to get 4x.

$$4x+14.2+4+1x+25.5$$

Add 14.2 and 4 to get 18.2.

$$4x+18.2+1x+25.5$$

Combine 4x and 1x to get 5x.

$$5x+18.2+25.5$$

Add 18.2 and 25.5 to get 43.7.

$$5x+43.7$$

Differentiate w.r.t. x

$$5$$

Steps Using Derivative Rule for Sum

Combine x and 2x to get 3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x-4+18.2+x+4+1x+25.5)$$

Add -4 and 18.2 to get 14.2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x+14.2+x+4+1x+25.5)$$

Combine 3x and x to get 4x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x+14.2+4+1x+25.5)$$

Add 14.2 and 4 to get 18.2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x+18.2+1x+25.5)$$

Combine 4x and 1x to get 5x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x+18.2+25.5)$$

Add 18.2 and 25.5 to get 43.7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x+43.7)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$5x^{1-1}$$

Subtract 1 from 1.

$$5x^{0}$$

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

$$5\times 1$$

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

$$5$$