8x^3+3y^3=11xy

Question

8x^3+3y^3=11xy

nothingwasthesame · Answer

I need to find the derivative

nothingwasthesame · Answer

And I would really like if someone helped explain the problem please

s4sensitiveandshy · Answer

with respect to x ??

nothingwasthesame · Answer

Yes

s4sensitiveandshy · Answer

ok. are you familiar with the power rule ??
$$8x^3+3y^3=11xy$$
just take the derivative of each term at left side 
and at right side apply the power rule.

nothingwasthesame · Answer

Um can you explain the power rule please

s4sensitiveandshy · Answer

hmm okay 
$$y = x^n $$ $$y'=n x^{n-1} $$ 


power rule: multiply the coefficient by the exponent and then subtract one from the exponent.

s4sensitiveandshy · Answer

$$y= 2x^5$$
for example the derivative of this function would be $$\frac{dy}{dx}= 2\cdot 5 x^{5-1} \frac{dx}{dx}$$
$$\frac{dy}{dx}= 10 x^{4} $$

nothingwasthesame · Answer

Ok thanks I got it now

s4sensitiveandshy · Answer

alright so what would be the derivative of 8x^3
and 3y^3 ??

nothingwasthesame · Answer

On the left 24x^2+9y^2=11y

nothingwasthesame · Answer

+11xdy with respect to the X ?

nothingwasthesame · Answer

^2 means it is supposed to be squared

s4sensitiveandshy · Answer

$$8x^3+9y^3=11xy$$
ignore the right side for a sec  
don't forget the notation $$24 x^2 \frac{dx}{dx} +9y^3=11xy$$
24x^2 dx/dx you're taking the derivative of x with respect x
so it would be dx/dx=1 
$$24 x^2 (1)+9y^2 \frac{dy}{dx}=11xy$$
we are taking the derivative of y with respect to x
so it should be 9y^2 dy/dx

s4sensitiveandshy · Answer

notation dy/dx or dx/dx

s4sensitiveandshy · Answer

no. for the right side we have to apply the product rule 
because it's a product of two variables 
11x times y
the product rule:$$f(x) * g(x) = f'(x) *g(x) + f(x) *g'(x)$$
Derivative  of 1st function times the 2nd function  + 1st function times the derivative of 2nd function

nothingwasthesame · Answer

So if I apply the product rule correctly I should get it ?

s4sensitiveandshy · Answer

you have to simplify at the end.
we are solving for dy/dx

nothingwasthesame · Answer

For me it's not so much the but the process but I think I got it  I just need to remember the steps and to simplify and I have to go now :(

nothingwasthesame · Answer

THE answer*

nothingwasthesame · Answer

Thanks for guiding me I think I got it now :)

s4sensitiveandshy · Answer

yw. and yes you should work on a lot of questions then you will end up memorizing these rules :)