Solve 2x+x^2+6sqrt{4}

$$2x+ { x }^{ 2 } +6 \sqrt{ 4 }$$

Evaluate

$$x^{2}+2x+12$$

Solution Steps

Calculate the square root of 4 and get 2.

$$2x+x^{2}+6\times 2$$

Multiply 6 and 2 to get 12.

$$2x+x^{2}+12$$

Differentiate w.r.t. x

$$2\left(x+1\right)$$

Steps Using Derivative Rule for Sum

Calculate the square root of 4 and get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x+x^{2}+6\times 2)$$

Multiply 6 and 2 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x+x^{2}+12)$$

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}.

$$2x^{1-1}+2x^{2-1}$$

Subtract 1 from 1.

$$2x^{0}+2x^{2-1}$$

Subtract 1 from 2.

$$2x^{0}+2x^{1}$$

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

$$2x^{0}+2x$$

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

$$2\times 1+2x$$

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

$$2+2x$$