∫

Chain Rule

★★★★☆Undergraduate

📖Definition

Differentiation of composite functions: derivative of outer times derivative of inner.

(d)/(dx)[f(g(x))] = f'(g(x)) · g'(x)

Chain rule

(dy)/(dx) = (dy)/(du) · (du)/(dx)

Leibniz notation

예제 1★★★☆☆

Find the derivative of f(x) = sin(x²).

f'(x) = 2xcos(x²)

예제 2★★★☆☆

Find the derivative of f(x) = e^(3x+1).

f'(x) = 3e^3x+1

Backpropagation algorithm

#analysis#calculus#chain-rule#differentiation