How do you find the derivative of # e^(xy)=x/y#?
1 Answer
Use the natural log on both side, separate the division into the difference of two logs, use the product rule on the left and the chain rule on the y terms.
Explanation:
Use the natural logarithm on both sides:
The inverse functions on the left cancel each other:
Division in the argument of a logarithm is the same as the difference between the dividend and the divisor:
Add #ln(y) to both sides:
Differentiate each term:
Use the product rule combined with the chain rule on the first term:
Use the chain rule on the second term:
The last term is trivial:
Subtract y from both sides:
Factor out
Make common denominators on both sides:
Multiply both sides by
Use the distributive property on the numerator and denominator: