Find dx/dy y=3xe^(-kx)

Math
Differentiate both sides of the equation.
Differentiate using the Power Rule which states that is where .
Differentiate the right side of the equation.
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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 .
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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.
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Since is constant with respect to , the derivative of with respect to is .
Simplify the expression.
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Move to the left of .
Rewrite as .
Rewrite as .
Rewrite as .
Simplify.
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Apply the distributive property.
Multiply by .
Reorder terms.
Reform the equation by setting the left side equal to the right side.
Solve for .
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Rewrite the equation as .
Reorder factors in .
Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Divide each term by and simplify.
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Divide each term in by .
Simplify .
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify .
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Factor out of .
Rewrite as .
Factor out of .
Rewrite negatives.
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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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