Solve y/6y^2

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

Evaluate

$$\frac{1}{6y}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(y^{1}\right)^{1}\times \frac{1}{6y^{2}}$$

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

$$1^{1}\left(y^{1}\right)^{1}\times \frac{1}{6}\times \frac{1}{y^{2}}$$

Use the Commutative Property of Multiplication.

$$1^{1}\times \frac{1}{6}\left(y^{1}\right)^{1}\times \frac{1}{y^{2}}$$

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

$$1^{1}\times \frac{1}{6}y^{1}y^{2\left(-1\right)}$$

Multiply 2 times -1.

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

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

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

Add the exponents 1 and -2.

$$1^{1}\times \frac{1}{6}\times \frac{1}{y}$$

Raise 6 to the power -1.

$$\frac{1}{6}\times \frac{1}{y}$$

Differentiate w.r.t. y

$$-\frac{1}{6y^{2}}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{6}\times \frac{1}{y})$$

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}.

$$-\frac{1}{6}y^{-1-1}$$

Do the arithmetic.

$$-\frac{1}{6}y^{-2}$$