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)

Answer 1

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

Answer 2

f1+g+f+g1 right

Answer 3

\[(fg)'=f'g+g'f\] with
\[f(x)=x^5, f'(x)=5x^4, g(x)=y, g'(x)=y'\]

Answer 4

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

Answer 5

almost

Answer 6

\[5x^4y^5+5x^5y^4y'=0\] solve for \(y'\)

Answer 7

so subtract the y over and turn everything negative?

Answer 8

you subtract \(5x^4y^5\) from both sides, then divide both sides by \(5x^5y^4\)

Answer 9

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

Answer 10

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

Answer 11

thanks

Answer 12

yw