Question

Find the equation of the tangent line to the curve y = sqrt (x+5) at the point (4,3)

Answer 1

dy/dx = (1/2(x+5)^(-1/2)
or
= 1/(2√(x+5) )
at (4,3)
dy/dx = 1/(2√9) = 1/6

y-3 = (1/6)(x-4)
6y-18 = x-4
x - 6y = -14
or y = (1/6)x + 7/3

Answer 2

Thanks! Sorry to bother you but do you know how I can get the same answer by solving using the definition of the derivative instead?

Answer 3

I used the derivative.

Do you want to find the derivative by "first principles" ?

Answer 4

Oh no that's okay
The steps you put include the chain rule version of the power rule right?