1.Differentiate: x^2y^3+x = y I got 2x(y^3)+3y^3(x^2)+1=y ... Is that right? I think maybe I did it wrong.
2.The following function may be veiwed as a composite function f(g(x)). Find f(x) and g(x).
1
x^2+2x-3
is f(x)= to 1, and g(x)= to x^2+2x-3? that seems too simple.
3. With this one I'm preatty sure ou need to find the first derivitive, but I don't really know how to go about it.
Assume 4x^3+2xy-y^3=1/2. What is the slope of the graph at the point [1/2,-1]?
-any help would be greatly appreciated thanks.
If that's meant to be 1 over the rest, and by "= to 1" you mean reciprocal i.e. f(x) = 1/x or x to power minus one, then no, it's correct and not too simple.
Edit:
Just in case a picture helps...
As with the first, differentiate throughout (not forgetting the chain rule), then plug in the x and y values for the given point. I'll put a pic.3. With this one I'm preatty sure ou need to find the first derivitive, but I don't really know how to go about it.
Assume 4x^3+2xy-y^3=1/2. What is the slope of the graph at the point [1/2,-1]?
-any help would be greatly appreciated thanks.
Edit:
... where
... is the product rule, and...
... the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).
Spoiler:
_________________________________________
Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!