Question

find the equation of the tangent line to f(x)=e^(x^2-x) at x=0

Answer 1

1) Find the derivative of f(x)=e^(x^2-x). This represents the slope of the T. L.
2) Substitute 0 for x in this derivative. The result is the slope of the T. L. at x=0.

What next?

Answer 2

Steps:
1) Find f'(x).
2) Plug in x = 0 into f'(x).

1)
f'(x) = e^(x^2 - x) * (x^2 - x)'
f'(x) = e^(x^2 - x) * (2x - 1)

2)
f'(0) = e^(0^2 - 0) * (2*0 - 1)
f'(0) = e^0 * (-1)
f'(0) = -1