Solve 1/4x^-2

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

Evaluate

$$\frac{x^{2}}{4}$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

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

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

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

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

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

Multiply -2 times -1.

$$\frac{1}{4}x^{2}$$

Differentiate w.r.t. x

$$\frac{x}{2}$$

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).

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

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}.

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

Simplify.

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