Calculus For Machine Learning Pdf Link < FREE • HACKS >
For a function ( f(x) ), the derivative ( f'(x) ) measures instantaneous rate of change.
[
f'(x) = \lim_h \to 0 \fracf(x+h) - f(x)h
] calculus for machine learning pdf link
In ML, ( x ) might be a weight, and ( f'(x) ) tells you how the loss changes if you tweak that weight. For a function ( f(x) ), the derivative
“Calculus” by Gilbert Strang (MIT)
“Calculus for Machine Learning” (lecture notes) “Calculus” by Gilbert Strang (MIT)
OpenStax “Calculus” (Volumes 1–3)
| Function | Derivative |
|----------|-------------|
| ( x^n ) | ( n x^n-1 ) |
| ( e^x ) | ( e^x ) |
| ( \ln x ) | ( 1/x ) |
| ( \sigma(x) = \frac11+e^-x ) | ( \sigma(x)(1-\sigma(x)) ) |
| ( \tanh(x) ) | ( 1 - \tanh^2(x) ) |
| ( \textReLU(x) = \max(0,x) ) | 0 if x<0, 1 if x>0 (undefined at 0, but subgradient 0..1) |
| Softmax ( p_i = \frace^z_i\sum_j e^z_j ) | ( p_i(\delta_ij - p_j) ) |
For a function ( f(x) ), the derivative ( f'(x) ) measures instantaneous rate of change.
[ f'(x) = \lim_h \to 0 \fracf(x+h) - f(x)h ]
In ML, ( x ) might be a weight, and ( f'(x) ) tells you how the loss changes if you tweak that weight.
“Calculus” by Gilbert Strang (MIT)
“Calculus for Machine Learning” (lecture notes)
OpenStax “Calculus” (Volumes 1–3)
| Function | Derivative | |----------|-------------| | ( x^n ) | ( n x^n-1 ) | | ( e^x ) | ( e^x ) | | ( \ln x ) | ( 1/x ) | | ( \sigma(x) = \frac11+e^-x ) | ( \sigma(x)(1-\sigma(x)) ) | | ( \tanh(x) ) | ( 1 - \tanh^2(x) ) | | ( \textReLU(x) = \max(0,x) ) | 0 if x<0, 1 if x>0 (undefined at 0, but subgradient 0..1) | | Softmax ( p_i = \frace^z_i\sum_j e^z_j ) | ( p_i(\delta_ij - p_j) ) |