Calculus – Implicit Differentiation – Tangent Line

By | October 31, 2016

Implicit Differentiation – Find the Tangent Line

In this tutorial students will learn to use implicit differentiation to solve a tangent line problem.  The student will create the tangent line equation at the point of tangency (1,0).  The students will then use an online graphing calculator to verify their analytical results.

Implicit Function

$x^2+sin(y)=xy^2+1$

Implicit Differentiation

$y'=\frac {dy}{dx}=\frac {-2x+y^2} {cos(y)-x2y}$

The student computes the expression for the slope by hand.  Next the student will substitue in the (x,y) values from the point of tangency (1,0).

Tangent Line Equation

$y=-2x+2$

Graphing Tool

Click the link below to use an interactive graphing calculator to verify the results.

Key Skills

Implicit Differentiation

A special case of the chain rule used when a function cannot be written as a function of x.

Slope Intercept Form

y=mx+b

Where m is the slope and b is the y-intercept.

Trigonometry

Evaluating trigonometric functions

Algebra

Factoring
Moving terms while keeping an equation balanced
Substitution
Order of Operations