The discussion focuses on finding the derivative dy/dx for the equation (2x - 10 + e)^(y + 8) = e^(x - 6) at the point (5, -9). The user initially miscalculated the derivative, leading to confusion about the correct answer, which is (2 + e)/e. The correct application of logarithmic differentiation and the treatment of e as a constant were clarified, resolving the misunderstanding regarding the differentiation process.
PREREQUISITESStudents studying calculus, particularly those focusing on implicit and logarithmic differentiation, as well as anyone needing clarification on derivative calculations involving constants.
Nope said:Homework Statement
(2x-10+e)^(y+8)=e^(x-6)
value of dy/dx at the point, (5,-9)
Homework Equations
The Attempt at a Solution
(y+8)ln(2x-10+e)=x-6
y' ln(2x-10+e)+(y+8)(2+e)/(2x-10+e)=1
ln(2*5-10+e)=1
y'+(-9+8)(2+e)/e=1
y'-(2+e)/e=1
y'=1+(2+e)/e
but the answer is (2+e)/e, I don't know where i went wrong..
derivative of ln(e^(x-6)), should be 1, right?