Differentiate #y^2 = 4ax# w.r.t #x# (Where a is a constant)?
1 Answer
Aug 2, 2017
# dy/dx = (2a)/(y) #
Explanation:
When we differentiate
However, we only differentiate explicit functions of
Example:
#d/dx(y^2) = d/dy(y^2)dy/dx = 2ydy/dx #
When this is done in situ it is known as implicit differentiation.
Now, we have:
# y^2=4ax \ \ \ # , the equation of a Parabola in standard form
Implicitly differentiating wrt
# d/dx y^2 = d/dx 4ax #
# :. 2ydy/dx = 4a #
# :. dy/dx = (4a)/(2y) #
# :. dy/dx = (2a)/(y) #