Question

...

Answer 1

product rule for this one

Answer 2

I got:

3x^2-x/-y+7y Not sure if this is correct.

Answer 3

\[3x^2y+x^3y'-1-7y'=0\] etc

Answer 4

\[x^3y'-7y'=1-3x^2y\]
\[y'=\frac{1-3x^2y}{x^3-7}\]
if my algebra is right

Answer 5

For -1, where dy or dx it should belong to?

Answer 6

-1 is the derivative of -x wrt x

Answer 7

is it clear what you are doing in these problems? you are thinking that
\[y=f(x),y'=f'(x)\]

Answer 8

so if you see for example
\[x^3y\] you think
\[x^3f(x)\] and use the product rule to find the derivative, getting
\[3x^2f(x)+x^3f'(x)\] but you write
\[3x^2y+x^3y'\]

Answer 9

This topic is totally new to me today. I am trying to get used to those problems, which is why I am practicing more problems like this.

Answer 10

the first part is finding the derivative, using product rule, quotient rule etc, but always thinking that y is some function of x , even though you don't know it. hence the "implicit" part, as in y is implicitly (rather than explicitly) a function of x

Answer 11

That makes sense.

Answer 12

hope so. good luck!

Answer 13

Thank you for your dedication and hard work here. I am grateful for having you.