How do you find a line tangent to another line?

Step-by-step explanation:

1) Find the first derivative of f(x). 2) Plug x value of the indicated point into f '(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.

Use the product rule! f(x) = (x^2)(e^5x) First times the derivative of the second, plus, second times the derivative of the first: (d/dx) f(x) = (x^2) d/dx(e^5x) + (e^5x) d/dx (x^2) what's the derivative of e^5x? well you have to chain rule for that: d/dx (e^5x) = (e^5x) (5) now what is the derivative of x^2? yup! just 2 d/dx (x^2) = 2 so what's f'(x)? Let's just plug in our derivatives f'(x) = (x^2) (e^5x) (5) + (e^5x)(2) tada!