Solve 2n^0/2n^2

$$\frac { 2 n ^ { 0 } } { 2 n ^ { 2 } }$$

Evaluate

$$\frac{1}{n^{2}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(2n^{0}\right)^{1}\times \frac{1}{2n^{2}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$2^{1}\left(n^{0}\right)^{1}\times \frac{1}{2}\times \frac{1}{n^{2}}$$

Use the Commutative Property of Multiplication.

$$2^{1}\times \frac{1}{2}\left(n^{0}\right)^{1}\times \frac{1}{n^{2}}$$

To raise a power to another power, multiply the exponents.

$$2^{1}\times \frac{1}{2}n^{0}n^{2\left(-1\right)}$$

Multiply 2 times -1.

$$2^{1}\times \frac{1}{2}n^{0}n^{-2}$$

To multiply powers of the same base, add their exponents.

$$2^{1}\times \frac{1}{2}n^{-2}$$

To multiply powers of the same base, add their exponents.

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

Add the exponents 1 and -1.

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

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

$$1n^{-2}$$

For any term t, t\times 1=t and 1t=t.

$$n^{-2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{2^{1}n^{0}}{2^{1}n^{2}}$$

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

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

Subtract 1 from 1.

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

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

$$n^{-2}$$

Differentiate w.r.t. n

$$-\frac{2}{n^{3}}$$

Steps Using Chain Rule

Cancel out 2 in both numerator and denominator.

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

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{1}{n^{2}})$$

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

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

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}.

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

Simplify.

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

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

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