Solve x/2/frac{3{x}}

$$\frac { \frac { x } { 2 } } { \frac { 3 } { x } }$$

Evaluate

$$\frac{x^{2}}{6}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(\frac{1}{2}x^{1}\right)^{1}\times \frac{1}{3\times \frac{1}{x}}$$

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

$$\left(\frac{1}{2}\right)^{1}\left(x^{1}\right)^{1}\times \frac{1}{3}\times \frac{1}{\frac{1}{x}}$$

Use the Commutative Property of Multiplication.

$$\left(\frac{1}{2}\right)^{1}\times \frac{1}{3}\left(x^{1}\right)^{1}\times \frac{1}{\frac{1}{x}}$$

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

$$\left(\frac{1}{2}\right)^{1}\times \frac{1}{3}x^{1}x^{-\left(-1\right)}$$

Multiply -1 times -1.

$$\left(\frac{1}{2}\right)^{1}\times \frac{1}{3}x^{1}x^{1}$$

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

$$\left(\frac{1}{2}\right)^{1}\times \frac{1}{3}x^{1+1}$$

Add the exponents 1 and 1.

$$\left(\frac{1}{2}\right)^{1}\times \frac{1}{3}x^{2}$$

Raise \frac{1}{2} to the power 1.

$$\frac{1}{2}\times \frac{1}{3}x^{2}$$

Multiply \frac{1}{2} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{1}{6}x^{2}$$

Differentiate w.r.t. x

$$\frac{x}{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{2}}{3}x^{1-\left(-1\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{6}x^{2})$$

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}.

$$2\times \frac{1}{6}x^{2-1}$$

Do the arithmetic.

$$\frac{1}{3}x^{1}$$

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

$$\frac{1}{3}x$$