Solve 1/-4n^-2

$$\frac { 1 } { - 4 n ^ { - 2 } }$$

Evaluate

$$-\frac{n^{2}}{4}$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

$$\frac{1}{-4n^{-2}}$$

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

$$\frac{1}{-4}\times \frac{1}{n^{-2}}$$

Raise -4 to the power -1.

$$-\frac{1}{4}\times \frac{1}{n^{-2}}$$

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

$$-\frac{1}{4}n^{-2\left(-1\right)}$$

Multiply -2 times -1.

$$-\frac{1}{4}n^{2}$$

Differentiate w.r.t. n

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

Steps Using Chain Rule

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).

$$-\left(-4n^{-2}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}n}(-4n^{-2})$$

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}.

$$-\left(-4n^{-2}\right)^{-2}\left(-2\right)\left(-4\right)n^{-2-1}$$

Simplify.

$$-8n^{-3}\left(-4n^{-2}\right)^{-2}$$