Question

Differentiate:

Answer 1

\[\LARGE y=\frac{4x^3-7x}{5x^2+2}\]

Answer 2

quotient rule

Answer 3

If I'm not mistaken you use quotient rule right?
So: \[\LARGE y'=\frac{(5x^2+2)(4x^3-7x)'-(5x^2+2)'(4x^3-7x)}{(5x^2+2)^2}\]

Answer 4

\[\huge\frac{ f(x)g'(x)-g(x)f'(x) }{f(x)^2}\]

Answer 5

you can also use product rule, which implements another rule

Answer 6

implicit differentiation
dy/dx y'=20x^4++59x^2-14/(5x^2+2)^2

Answer 7

y' = 4x^3 - 7x * (5x^2 + 2)^(-1)

Answer 8

whichever you are most comfortable with
you can even differentiate using the definition

Answer 9

u already know how to do dis

Answer 10

Thanks guys
@shamil98 Shh xD

Answer 11

I'm curious as to the implicit differentiation approach tho.

Answer 12

just like the other rules or ways of solving it, it would not be optimal to do so
besides, implicit differentiation just means you are waiting for the value of the unknown, which in this case is the x
y = x^2
y' = 2x * x'

Answer 13

\(5x^2y+2y-4x^3+7x=0\) now use implicit

Answer 14

Oh, now I see.