determine dy/dx by implicit differentiation
5x^2y-sin(x^2+y^2)-2x=0

Question

determine dy/dx by implicit differentiation
5x^2y-sin(x^2+y^2)-2x=0

.sam. · Answer

Where are you stucked?

anonymous · Answer

by implicit differentiation... kind of wondering if this is the chain rule...

anonymous · Answer

i'm not too good with this stuff

mathmale · Answer

Apply the derivative operator to the implicit equation that you've typed in:$$\frac{ d }{ dx }(5x ^{2}y-\sin(x^2+y^2)-2x=0)$$

mathmale · Answer

Implicit diff'n almost always involves the chain rule, but is not the chain rule.
the first term inside the parentheses is 5x^2*y, which we should recognize as being a product.

so we'll have to apply the product rule here, and, by the way, also the chain rule on that y. 

Can you find $$\frac{ d }{ dx  }5x^2y?$$

anonymous · Answer

i think that is 10xy

mathmale · Answer

If you had applied the product rule, you would have obtained a result with two terms.

$$\frac{ d }{ dx }5x^2y=5(x^2\frac{ dy }{ dx }+y(2x))$$Please look this over carefully and determine how much sense (or how little) it makes to you.

mathmale · Answer

Some people write the product rule as 
(uv)' = uv' + vu'

which is nice and short.

anonymous · Answer

okay that makes sense above. now what about the -2x? does that end up becoming,

5(2xy+x^2(dy/dx)-2?