## Find an equation to the tangent line to a curve and parrallel

1. The problem statement, all variables and given/known data

Find an equation of the tangent line to the curve y = x√x that is parallel to the line
y = 1+3x.

2. Relevant equations

m = 3

3. The attempt at a solution

Here is my attempt: dy/dx(x) * dy/dx(x^(1/2)) = (1) * (1/2x^(-1/2)) = (1/2x^(-1/2))

(1/2x^(-1/2)) = 3 → x^(-1/2) = 6 → -√x = 6

x = -√36 = 6 → -6=6 -1=1

Thank you, I will not be able to respond for a bit as im leaving for home now.
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 Quote by foreverlost 1. The problem statement, all variables and given/known data Find an equation of the tangent line to the curve y = x√x that is parallel to the line y = 1+3x. 2. Relevant equations m = 3 3. The attempt at a solution Here is my attempt: dy/dx(x) * dy/dx(x^(1/2)) = (1) * (1/2x^(-1/2)) = (1/2x^(-1/2)) (1/2x^(-1/2)) = 3 → x^(-1/2) = 6 → -√x = 6 x = -√36 = 6 → -6=6 -1=1 Thank you, I will not be able to respond for a bit as im leaving for home now.
Two comments. First, why on earth would you not simplify ##x\sqrt x## to ##x^\frac 3 2## before you differentiate? And given that you didn't, the product rule for differentiation is not ##(fg)' = f'g'##, which is what you did. Try again.

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To add to what LCKurtz said about your oversimplification of the product rule, what you wrote does not mean what you think.
 Quote by foreverlost dy/dx(x) * dy/dx(x^(1/2))
You don't take "dy/dx of x" or "dy/dx of x^(1/2)." You can take the derivative with respect to x of something, which you write as d/dx(x) + d/dx(x^(1/2)).

The expression dy/dx(x) means dy/dx times x, which I'm pretty sure isn't what you intended.