Solve (x+1)lceil3rceil

$$(x+1) \lceil 3 \rceil$$

Evaluate

$$3\left(x+1\right)$$

Solution Steps

The ceiling of a real number a is the smallest integer number greater than or equal to a. The ceiling of 3 is 3.

$$\left(x+1\right)\times 3$$

Use the distributive property to multiply x+1 by 3.

$$3x+3$$

Differentiate w.r.t. x

$$3$$

Steps Using Derivative Rule for Sum

The ceiling of a real number a is the smallest integer number greater than or equal to a. The ceiling of 3 is 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x+1\right)\times 3)$$

Use the distributive property to multiply x+1 by 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x+3)$$

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}.

$$3x^{1-1}$$

Subtract 1 from 1.

$$3x^{0}$$

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

$$3\times 1$$

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

$$3$$