Solve frac{8nsqrt{4n^2}}{2nsqrt{16}}

$$\frac { 8 n \sqrt { 4 n ^ { 2 } } } { 2 n \sqrt { 16 } }$$

Differentiate w.r.t. n

$$2sign(n)$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{8\sqrt{4n^{2}}}{2\sqrt{16}}n^{1-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}n}(2|n|n^{0})$$

For any number a except 0, a^{0}=1.

$$\frac{\mathrm{d}}{\mathrm{d}n}(2|n|)$$

The derivative of a constant term is 0.

$$0$$

Evaluate

$$2|n|$$