$$ h'(y)= \tanh(4y)+4y\, sech^2(4y) .$$
Work Step by Step
Since $ h(y)=y\tanh(4y)$, then the derivative, by using the product rule, is given by $$ h'(y)=\tanh(4y)+y\, sech^2(4y) (4y)'=\tanh(4y)+4y\, sech^2(4y) .$$
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