Up to now, we’ve been differentiating functions defined for f(x) in terms of x, or equations defined for y in terms of x. In other words, every equation we’ve differentiated has had the variables separated on either side of the equal sign. For instance, the equation y=3x^2+2x+1 has the y variable on the left side, and the x variable on the right side. We don’t have x and y variables mixed together on the left, and they aren’t mixed together on the right, either.
Read MoreRemember that we’ll use implicit differentiation to take the first derivative, and then use implicit differentiation again to take the derivative of the first derivative to find the second derivative. Once we have an equation for the second derivative, we can always make a substitution for y, since we already found y' when we found the first derivative.
Read MoreTo find the equation of the tangent line using implicit differentiation, follow three steps. First differentiate implicitly, then plug in the point of tangency to find the slope, then put the slope and the tangent point into the point-slope formula.
Read MoreMost often in calculus, you deal with explicitly defined functions, which are functions that are solved for y in terms of x.
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