equation of tangent at (0,4) on x(y^3)+y+7(x^4) = 4

find the equation of the tangent at (0,4) on x(y^3)+y+7(x^4) = 4

first differentiate the given equation w.r.t.x (implicit differentiation) and extract dy/dx
evaluate dy/dx at (0,4) to get the slope m of the tangent to the curve at (0,4)
use point slope form of a straight line to get the equation of the tangent
other examples:
find the equation of the tangent at (1,1) on x²+y²+xy-3=0 ----tangent on a curve
equation of the tangent at (1,1) on x² +xy+2y² = 4 -----------equation of tangent using calculus
equation of tangent to y =x^4 at the point where x=2
equation of tangent at (e,e) on y = x lnx
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equation of tangent at (e,e) on y = x lnx

y = x lnx

dy/dx = x(1/x) + lnx (1) = 1 + lnx

slope of tangent , m = (dy/dx) at (e,e) = 1 + ln(e) = 1 + 1 = 2

equation of tangent at (e,e) is
(y - y1) = m (x-x1)

y - e = 2(x-e)

or y = 2x - e
other examples
equation of tangent to y =x^4 at the point where x=2


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