Question

someone help me implicitly derive this function

Answer 1

\[xy^4+x^2y=x+3y\]

Answer 2

do you know how to take derivative ??
u just need to take derivative of each term. solve for y with respect to x

Answer 3

I've gotten this far

\[\frac{ dy }{ dx }(y^4+x^2+6xy)=1+3\frac{ dy }{ dx }\]

im not sure how to finish solving for dy/dx

Answer 4

hmm that doesn't look good
there is the product so you should use product rule \[\huge \rm x \cdot y^4+x^2 \cdot y=x+3y\]

Answer 5

\[\large\rm x \cdot y^4\]
product rule
\[\large\rm \color{Red}{f} \cdot g = \color{red}{f'} g +g'\color{red}{f}\]
so \[\large\rm \color{Red}{ x} \ \cdot y^4 = \color{Red}{1 \frac{dx}{dx}} y^4 + 4y^3 \frac{dy}{dx} \color{Red}{(x)}\]
dx/dx cancels out
\[\rm y^4+4xy^3 \frac{dy}{dx}\]

Answer 6

yeah I did use product rule , then I factored out the dy/dx and I added like terms

Answer 7

ohh okay let me check

Answer 8

i didn't get any like terms can you please show the work ??

Answer 9

\[((1)(y^4)+x(4y^3)\frac{ dy }{ dx })+(2xy+x^2(1)\frac{ dy }{ dx })=1+3\frac{ dy }{ dx }\]

=> \[\frac{ dy }{ dx }(y^4+4xy+2xy+x^2)=1+3\frac{ dy }{ dx }\]

Answer 10

I differentiated and setup the product rule and and then I factored out the dy/dx and was left with 4xy and 2xy as like terms so I added them

Answer 11

oh , I made and error, the 4xy is actually 4xy^4

Answer 12

no its actually 4xy^3
derivative of y^4 is 4y^3

Answer 13

so you can't combine them