Differentiate both sides of the equation.

The derivative of with respect to is .

By the Sum Rule, the derivative of with respect to is .

Evaluate .

Since is constant with respect to , the derivative of with respect to is .

Rewrite as .

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

Differentiate using the Power Rule which states that is where .

Replace all occurrences of with .

Differentiate using the Power Rule which states that is where .

Multiply the exponents in .

Apply the power rule and multiply exponents, .

Multiply by .

Multiply by .

Multiply by by adding the exponents.

Move .

Use the power rule to combine exponents.

Subtract from .

Move to the left of .

Evaluate .

Since is constant with respect to , the derivative of with respect to is .

Differentiate using the Exponential Rule which states that is where =.

Rewrite the expression using the negative exponent rule .

Simplify.

Combine terms.

Combine and .

Combine and .

Move to the left of .

Move the negative in front of the fraction.

Reorder terms.

Reform the equation by setting the left side equal to the right side.

Reorder factors in .

Replace with .

Find dz/dy z=A/(y^14)+Be^y