differentiate the equationy=tan[ln(ax+b)]

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cosinusix | College Teacher | (Level 3) Assistant Educator

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y is a composite function in the form `y=f(g(x))` with `f(X)=tan(X)` and `g(x)=ln(ax+b)` .







then` y'=g'(x)*f'(g(x))=a/(ax+b)*(1+tan^2(ln(ax+b)))`


The derivative is



Remark. There is a second expression for the derivative of tan X:


It is the same function but written with a different expression. Using this expression in the derivative of the composite fonction we find a different expression of the same derivative:



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