Solve 4(1)^2-x+1+3

$$4 ( 1 ) ^ { 2 } - x + 1 + 3$$

Evaluate

$$8-x$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

$$4\times 1-x+1+3$$

Multiply 4 and 1 to get 4.

$$4-x+1+3$$

Add 4 and 1 to get 5.

$$5-x+3$$

Add 5 and 3 to get 8.

$$8-x$$

Differentiate w.r.t. x

$$-1$$

Steps Using Derivative Rule for Sum

Calculate 1 to the power of 2 and get 1.

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

Multiply 4 and 1 to get 4.

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

Add 4 and 1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5-x+3)$$

Add 5 and 3 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8-x)$$

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}.

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

Subtract 1 from 1.

$$-x^{0}$$

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

$$-1$$