# Find dx/dy y=3xe^(-kx) Differentiate both sides of the equation.
Differentiate using the Power Rule which states that is where .
Differentiate the right side of the equation.
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Product Rule which states that is where and .
Differentiate using the chain rule, which states that is where and .
To apply the Chain Rule, set as .
Differentiate using the Exponential Rule which states that is where =.
Replace all occurrences of with .
Differentiate using the Constant Multiple Rule.
Since is constant with respect to , the derivative of with respect to is .
Simplify the expression.
Move to the left of .
Rewrite as .
Rewrite as .
Rewrite as .
Simplify.
Apply the distributive property.
Multiply by .
Reorder terms.
Reform the equation by setting the left side equal to the right side.
Solve for .
Rewrite the equation as .
Reorder factors in .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Divide each term by and simplify.
Divide each term in by .
Simplify .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify .
Factor out of .
Rewrite as .
Factor out of .
Rewrite negatives.
Rewrite as .
Move the negative in front of the fraction.
Reorder factors in .
Replace with .
Find dx/dy y=3xe^(-kx)

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