Question

Find the slope of the tangent line to the exponential function at the point (0,1) y=e^x/3

Answer 1

The slope of a function is simply equal to its first derivative. So let us first take the 1st derivative of the equation:

y = e^(x / 3)

dy / dx = e^(x / 3) (1 / 3)

At x = 0:

dy / dx = slope = e ^(0) (1/3)

slope = 1/3