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

## Homework Statement

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

m = 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.

LCKurtz
Science Advisor
Homework Helper
Gold Member

## Homework Statement

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

m = 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.

Last edited:
Mark44
Mentor
To add to what LCKurtz said about your oversimplification of the product rule, what you wrote does not mean what you think.
foreverlost said:
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.