Unlocking the chain rule through the derivative of ln(a^x)
In short: Mastering the chain rule is a cornerstone of calculus. This lesson breaks down how to differentiate a composite function, specifically the natural logarithm of an exponential expression.
The video demonstrates how to find the derivative of f(x) = ln(a^x). Because this function is a composition of the natural logarithm ln(x) and the exponential function a^x, it requires the application of the chain rule.
The tutorial is presented by Bill Scott, a member of the team that developed Khan Academy’s AP lessons. It provides a clear, step-by-step worked example designed for students preparing for AP Calculus AB.
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Sources
- Summary by Intellect · source: Worked example: Derivative of ln(ÃÂx) using the chain rule | AP Calculus AB | Khan Academy
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