I don't see what y^x has to do with your original equation. y^x is not anything like e^y and yes, you should use the chain rule. But the chain rule does NOT give "ye^{y-1}"!brambleberry said:Homework Statement
What is the derivative of e^y? i think i am differentiating with respect to x
Homework Equations
Derivative of y^x is y^x
The Attempt at a Solution
I don't know if I should use the chain rule or treat it like y^x. When i used the chain rule I got ye^y-1, but then I wondered if it should be e^y.
The derivative of e^y is e^y, also known as the natural logarithm, or ln.
To solve for the derivative of e^y using the Chain Rule, you must first rewrite the expression in terms of x. Then, apply the Chain Rule by taking the derivative of the outer function (e^y) and multiplying it by the derivative of the inner function (y'). This can be written as d/dx (e^y) = e^y * y'.
Yes, for example, if we have the expression e^2x, we can rewrite it as e^(2x) = (e^2)^x. Then, using the Chain Rule, we get d/dx (e^2x) = e^(2x) * 2 = 2e^(2x).
The Chain Rule allows us to find the derivative of more complex functions, such as e^y, by breaking them down into simpler functions and applying the derivative rules. It is especially useful when dealing with exponential functions.
Yes, there are other methods such as using logarithmic differentiation or using the power rule for derivatives. However, the Chain Rule is the most efficient method for solving for the derivative of e^y.