Find the value of y' when x
O if
xy^8 + e^y/5 =
= e.

It looks like the given equation says

When x = 0, you have

Differentiating both sides with respect to x gives

That is, the derivative operator distributes over sums, and the derivative of a constant is 0; apply the product rule on the first term and chain rule on the second; then use chain rule one more time.

Now plug in x = 0 and y = 5, and solve for y' :

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.