Solve {left(sqrt{x^2-4^2}right)}^2

$${ \left( \sqrt{ { x }^{ 2 } - { 4 }^{ 2 } } \right) }^{ 2 }$$

Evaluate

$$x^{2}-16$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\left(\sqrt{x^{2}-16}\right)^{2}$$

Calculate \sqrt{x^{2}-16} to the power of 2 and get x^{2}-16.

$$x^{2}-16$$

Differentiate w.r.t. x

$$2x$$

Steps Using Derivative Rule for Sum

Calculate 4 to the power of 2 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(\sqrt{x^{2}-16}\right)^{2})$$

Calculate \sqrt{x^{2}-16} to the power of 2 and get x^{2}-16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-16)$$

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}.

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

Subtract 1 from 2.

$$2x^{1}$$

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

$$2x$$