Question

The derivative of y = ln(ax+b)

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{y=log_{\,e}(ax+b)}$

$\underline{\textbf{To find:}}$

$\mathsf{Derivative\;of\;y=log_{\,e}(ax+b)}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{y=log_{\,e}(ax+b)}$

$\textsf{Differentiate with respect to 'x'}$

$\mathsf{\dfrac{dy}{dx}=\dfrac{1}{ax+b}\,\dfrac{d(ax+b)}{dx}}$

$\mathsf{\dfrac{dy}{dx}=\dfrac{1}{ax+b}(a)}$

$\implies\boxed{\mathsf{\dfrac{dy}{dx}=\dfrac{a}{ax+b}}}$

$\underline{\textbf{Find more:}}$

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