Calculus

Many students struggle with the Chain Rule because they get lost in the notation of f(g(x)) and dy/dx = (dy/du) * (du/dx). Let's break down what it actually means in plain English.

Many students simply memorize the Integration by Parts formula: ∫ u dv = uv - ∫ v du, but understanding where it comes from makes it much easier to remember and apply during exams.

1. The Intuitive Proof (Reverse Product Rule)

The entire concept is actually just the Product Rule for differentiation in reverse.
From the product rule for two differentiable functions, u and v: (uv)' = u'v + uv'

Hello, can anyone solve this equation?

I can't figure it out,

$(1-xy)^{-2} dx + \left[ y^2 + x^2 (1-xy)^{-2} \right] dy = 0$

Thanks.

Can anyone solve this D. E.?

y' = x^3 - 2xy, where y(1)=1

and

y' = 2(2x-y) that passes through (0,1)