Solve 5-n^2+2sqrt{(5-n^2)(0)}

$$5 - n ^ { 2 } + 2 \sqrt { ( 5 - n ^ { 2 } ) ( 0 ) }$$

Evaluate

$$5-n^{2}$$

Solution Steps

Anything times zero gives zero.

$$5-n^{2}+2\sqrt{0}$$

Calculate the square root of 0 and get 0.

$$5-n^{2}+2\times 0$$

Multiply 2 and 0 to get 0.

$$5-n^{2}+0$$

Add 5 and 0 to get 5.

$$5-n^{2}$$

Differentiate w.r.t. n

$$-2n$$

Steps Using Derivative Rule for Sum

Anything times zero gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}n}(5-n^{2}+2\sqrt{0})$$

Calculate the square root of 0 and get 0.

$$\frac{\mathrm{d}}{\mathrm{d}n}(5-n^{2}+2\times 0)$$

Multiply 2 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}n}(5-n^{2}+0)$$

Add 5 and 0 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}n}(5-n^{2})$$

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}.

$$2\left(-1\right)n^{2-1}$$

Multiply 2 times -1.

$$-2n^{2-1}$$

Subtract 1 from 2.

$$-2n^{1}$$

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

$$-2n$$