Differentiate the expression x^5y^5 with respect to x. (Use D for dy/dx).
Why do I not get this would it not be (5x^4)/(5y^4)

Question

Differentiate the expression x^5y^5 with respect to x. (Use D for dy/dx).
Why do I not get this would it not be (5x^4)/(5y^4)

anonymous · Answer

you need the product rule for this because it is a product

anonymous · Answer

f1+g+f+g1 right

anonymous · Answer

$$(fg)'=f'g+g'f$$ with 
$$f(x)=x^5, f'(x)=5x^4, g(x)=y, g'(x)=y'$$

anonymous · Answer

(5x^4)(y^5)+(x^5)(5y^4)

anonymous · Answer

almost

anonymous · Answer

$$5x^4y^5+5x^5y^4y'=0$$ solve for $y'$

anonymous · Answer

so subtract the y over and turn everything negative?

anonymous · Answer

you subtract $5x^4y^5$ from both sides, then divide both sides by $5x^5y^4$

anonymous · Answer

so -5x^5y^4/5x^5y^4

anonymous · Answer

If it is given x^5y^5=0,then
$$5x ^{4}y ^{5}+x ^{5}*5y ^{4} D=0$$
$$5x ^{5}y ^{4}D=-5x ^{4}y ^{5}$$
$$D=-\frac{ 5x ^{4}y ^{5} }{ 5x ^{5}y ^{4} }=-\frac{ y }{ x }$$

anonymous · Answer

thanks

anonymous · Answer

yw