Solve 1div2/x^5

$$1 \div \frac { 2 } { x ^ { 5 } }$$

Evaluate

$$\frac{x^{5}}{2}$$

Steps for Raising Quotient to a Power

Use the rules of exponents to simplify the expression.

$$\frac{1}{\frac{2}{x^{5}}}$$

To raise the quotient of two numbers to a power, raise each number to the power and then divide.

$$\frac{1}{2\times \frac{1}{x^{5}}}$$

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

$$\frac{\frac{1}{2}}{x^{5\left(-1\right)}}$$

Multiply 5 times -1.

$$\frac{\frac{1}{2}x^{5}}{1}$$

Differentiate w.r.t. x

$$\frac{5x^{4}}{2}$$

Steps Using Definition of a Derivative

Divide 1 by \frac{2}{x^{5}} by multiplying 1 by the reciprocal of \frac{2}{x^{5}}.

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

The derivative of ax^{n} is nax^{n-1}.

$$5\times \frac{1}{2}x^{5-1}$$

Multiply 5 times \frac{1}{2}.

$$\frac{5}{2}x^{5-1}$$

Subtract 1 from 5.

$$\frac{5}{2}x^{4}$$