Solve f(x)=(sqrt{x}+4)(sqrt{x}-4)

$$f ( x ) = ( \sqrt { x } + 4 ) ( \sqrt { x } - 4 )$$

Evaluate

$$x-16$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

$$x-4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$x-16$$

Differentiate w.r.t. x

$$1$$

Steps Using Derivative Rule for Sum

Consider \left(\sqrt{x}+4\right)\left(\sqrt{x}-4\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x-4^{2})$$

Calculate 4 to the power of 2 and get 16.

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

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}.

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

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

$$1$$