find dy/dx by implicit differentiation 4+9x = sin(x*y^4)?

Question

find dy/dx by implicit differentiation 4+9x = sin(x*y^4)

Answer 1

4+9x = sin(x*y^4)
Differentiate with respect to x:
9 = cos(xy^4) * (d/dx)(xy^4)
9 = cos(xy^4) [ x* 4y^3 dy/dx + y^4 ]
Now solve for dy/dx:
9 / cos(xy^4) = 4xy^3 dy/dx + y^4
9 / cos(xy^4) - y^4 = 4xy^3 dy/dx
dy/dx = [ 9 / cos(xy^4) - y^4 ] / 4xy^3
= [ 9 / 4xy^3 cos(xy^4) ] - y / 4x.

Answer 2

dy/dx[4+9x = sin(xy^2)]: 0+9 = cos(xy^2)*(y^2+2xy(dy/dx)) Chain and product rule 9 = y^2cos(xy^2) + 2xycos(xy^2)dy/dx dy/dx(2xycos(xy^2)) = 9 - y^2cos(xy^2) dy/dx = [9 - cos(xy^2) * y^2] / [cos(xy^2) * 2xy] it really is the answer i'm getting, yet i do not see a way of simplifying it any further. i imagine your mission develop into you probably did the spinoff of the interior (xy^2). The product rule is largely (fg)' = f'g + fg'

Answer 3

9dx/dx=cos(xy^4)(y^4dx/dx+4xy^3dy/dx)
now solve this for dy/dx=[9/cos(xy^4)-y^4]/(4xy^3)