SOLUTION: Y=[15e^(-x)]/[x+e^(-2x)] Solve dy/dx

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Question 1133146: Y=[15e^(-x)]/[x+e^(-2x)]
Solve dy/dx
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y=%2815e%5E%28-x%29%29%2F%28x%2Be%5E%28-2x%29%29
y=%2815%281%2Fe%5Ex%29%29%2F%28x%2B1%2Fe%5E%282x%29%29
y=%2815%2Fe%5Ex%29%2F%28%28x%2Ae%5E%282x%29%2B1%29%2Fe%5E%282x%29%29
y=%2815e%5E%282x%29%29%2F%28x%2Ae%5Ex%2A%28e%5E%282x%29%2B1%29%29
y=%2815e%5Ex%29%2F%28%28x%2Ae%5E%282x%29%2B1%29%29

Solve dy%2Fdx+

%28dy%2Fdx%29%28%2815e%5Ex%29%2F%28x%2Ae%5E%282+x%29+%2B+1%29%29 = > first take the constant out


Apply the Quotient Rule: f%2Fg'=(f'*g-g'*+f)/g%5E2



Apply the common derivative:
%28d%2Fdx%29e%5Ex=e%5Ex

%28d%2Fdx%29%28xe%5E%282x%29%2B1%29=e%5E%282x%29%2B2e%5E%282x%29%2Ax




simplify:


since
we have