Solve 6.8x-11.2+32x-11.2+6.8+3.2

$$6.8 x - 11.2 + 32 x - 11.2 + 6.8 + 3.2$$

Evaluate

$$\frac{194x-62}{5}$$

Solution Steps

Combine 6.8x and 32x to get 38.8x.

$$38.8x-11.2-11.2+6.8+3.2$$

Subtract 11.2 from -11.2 to get -22.4.

$$38.8x-22.4+6.8+3.2$$

Add -22.4 and 6.8 to get -15.6.

$$38.8x-15.6+3.2$$

Add -15.6 and 3.2 to get -12.4.

$$38.8x-12.4$$

Differentiate w.r.t. x

$$38.8$$

Steps Using Derivative Rule for Sum

Combine 6.8x and 32x to get 38.8x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(38.8x-11.2-11.2+6.8+3.2)$$

Subtract 11.2 from -11.2 to get -22.4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(38.8x-22.4+6.8+3.2)$$

Add -22.4 and 6.8 to get -15.6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(38.8x-15.6+3.2)$$

Add -15.6 and 3.2 to get -12.4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(38.8x-12.4)$$

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}.

$$38.8x^{1-1}$$

Subtract 1 from 1.

$$38.8x^{0}$$

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

$$38.8\times 1$$

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

$$38.8$$