Implicit differentiation
In calculus, implicit differentiation, an application of the Chain Rule, allows one to differentiate implicit functions. Consider y + x = -4. This function can be differentiated normally by using algebra to change this equation to an explicit function: f(x) = y = −x - 4; such differentiation would result in a value of −1. Likewise, one can use implicit differentiation; dy/dx + dx/dx = 0 = dy/dx + 1; dy/dx = -1. Implicit differentiaton is used when the user cannot, or choses not to, use algebra to manipulate an implicit function, until it becomes explicit.An example of an implicit function, for which implicit differentiation might be easier than attempting to use explicit differentiation, is: x4 + 2y2 = 8. In order to explicitly differentiate this, one would have to obtain (via algebra) f(x) = {−[√(8 - x4)] / 2}, and then differentiate f(x). One might find it substantially easier to implicitly differentiate the implicit function; 4x3 + 4y(dy/dx) = 0; thus, dy/dx = −4x3 / 4y = −x3 / y.
He needed me--then--so dreadfully!
BIGELOW--And is it that keeps driving him on now?
MARTHA--Oh, no. He's found himself. His work has taken the place
work has me in it, I like to think.html">think--and I have him.
BIGELOW--[Shaking his head.] I think people are foolish to stand
a great comfort in one's old age.html">age, I've/ve.html">ve tritely found.
MARTHA--[Smiling.] Old age!
BIGELOW--I'm knocking at the door of fatal forty.
MARTHA--[With forced gaiety.] You're not very tactful, I must say.
thirty yet.
MARTHA--[Laughing.] After that nice remark I'll have to forgive
is a slender, rather pretty girl of twenty-five. The stamp of
on a superior, intellectual air, is full of nervous, thwarted
eyebrows are raised.]
LILY--[Coming into the room--breezily.] Hello, Martha. Hello, Big.
regardless. Hope I'm not interrupting.
MARTHA--Not at all.
LILY--[Sitting down by the table as MARTHA and BIGELOW resume
you tell Big you'd forgive him everything, Martha. [Dryly--with a
proposition.
BIGELOW--[Displeased but trying to smile it off.] The past is
BIGELOW gets up.] If you want to reward me for my truthfulness,
know it's an imposition but they've grown to expect you. [Glancing
then pick you up here. Is that all right?
MARTHA--Fine.
BIGELOW--I'll run, then. Good-by, Lily. [She nods. BIGELOW goes
You were forgetting, weren't you?
MARTHA--What?
LILY--That you'd invited all the family over here to tea this
studied carelessness.] Do you like Bigelow?
MARTHA--Yes, very much. And Curt thinks the world of.
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