Solve (x(5))+((x+11))(1)=

$$(x(5))+((x+11))(1)=$$

Evaluate

$$6x+11$$

Solution Steps

Use the distributive property to multiply x+11 by 1.

$$x\times 5+x+11$$

Combine x\times 5 and x to get 6x.

$$6x+11$$

Differentiate w.r.t. x

$$6$$

Steps Using Derivative Rule for Sum

Use the distributive property to multiply x+11 by 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 5+x+11)$$

Combine x\times 5 and x to get 6x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x+11)$$

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}.

$$6x^{1-1}$$

Subtract 1 from 1.

$$6x^{0}$$

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

$$6\times 1$$

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

$$6$$