Solve 3(sqrt{x^2+3})^2

$$3 ( \sqrt { x ^ { 2 } + 3 } ) ^ { 2 }$$

Evaluate

$$3\left(x^{2}+3\right)$$

Solution Steps

Calculate \sqrt{x^{2}+3} to the power of 2 and get x^{2}+3.

$$3\left(x^{2}+3\right)$$

Use the distributive property to multiply 3 by x^{2}+3.

$$3x^{2}+9$$

Differentiate w.r.t. x

$$6x$$

Steps Using Derivative Rule for Sum

Calculate \sqrt{x^{2}+3} to the power of 2 and get x^{2}+3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3\left(x^{2}+3\right))$$

Use the distributive property to multiply 3 by x^{2}+3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}+9)$$

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}.

$$2\times 3x^{2-1}$$

Multiply 2 times 3.

$$6x^{2-1}$$

Subtract 1 from 2.

$$6x^{1}$$

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

$$6x$$