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| 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) ) |