# Tangent line to the curve.

• March 16th 2010, 06:10 PM
Zanderist
Tangent line to the curve.
How do I do the following.

find the equation of the tangent line to the curve:

$xy^3+xy=14$

At point (7,1).
• March 16th 2010, 06:16 PM
pickslides
Quote:

Originally Posted by Zanderist
How do I do the following.

find the equation of the tangent line to the curve:

$xy^3+xy=14$

At point (7,1).

$x(y^3+y)=14$

$x=\frac{14}{y^3+y}$

Now find $\frac{dx}{dy}$ at $y = 1$
• March 16th 2010, 06:16 PM
skeeter
Quote:

Originally Posted by Zanderist
How do I do the following.

find the equation of the tangent line to the curve:

$xy^3+xy=14$

At point (7,1).

find $\frac{dy}{dx}$ in terms of $x$ and $y$, then sustitute $7$ for $x$ and $1$ for $y$ in the derivative expression to find the slope at that point.