Solve h/2divh^2/2

$$\frac { h } { 2 } \div \frac { h ^ { 2 } } { 2 }$$

Evaluate

$$\frac{1}{h}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 2 times -1.

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

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

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

Add the exponents 1 and -2.

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

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

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

Add the exponents 1 and -1.

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

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

$$1\times \frac{1}{h}$$

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

$$\frac{1}{h}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{\left(\frac{1}{2}\right)^{1}h^{1}}{\left(\frac{1}{2}\right)^{1}h^{2}}$$

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

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

Subtract 1 from 1.

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

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

$$h^{1-2}$$

Subtract 2 from 1.

$$\frac{1}{h}$$

Differentiate w.r.t. h

$$-\frac{1}{h^{2}}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{1}{h})$$

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}.

$$-h^{-1-1}$$

Do the arithmetic.

$$-h^{-2}$$