Solve 68x-11.2+32x-11.1+68+3.2

$$68 x - 11.2 + 32 x - 11.1 + 68 + 3.2$$

Evaluate

$$100x+48.9$$

Solution Steps

Combine 68x and 32x to get 100x.

$$100x-11.2-11.1+68+3.2$$

Subtract 11.1 from -11.2 to get -22.3.

$$100x-22.3+68+3.2$$

Add -22.3 and 68 to get 45.7.

$$100x+45.7+3.2$$

Add 45.7 and 3.2 to get 48.9.

$$100x+48.9$$

Differentiate w.r.t. x

$$100$$

Steps Using Derivative Rule for Sum

Combine 68x and 32x to get 100x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(100x-11.2-11.1+68+3.2)$$

Subtract 11.1 from -11.2 to get -22.3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(100x-22.3+68+3.2)$$

Add -22.3 and 68 to get 45.7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(100x+45.7+3.2)$$

Add 45.7 and 3.2 to get 48.9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(100x+48.9)$$

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}.

$$100x^{1-1}$$

Subtract 1 from 1.

$$100x^{0}$$

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

$$100\times 1$$

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

$$100$$