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In fact this technique can help us find derivatives in many situations, not just when we seek the derivative of an inverse function. Derivative of the Logarithm Function y ln x. Rather than relying on pictures for our understanding, we would like to be able to exploit this relationship computationally. Section 4.7 Implicit and Logarithmic Differentiation ¶ Subsection 4.7.1 Implicit Differentiation ¶Īs we have seen, there is a close relationship between the derivatives of \(\ds e^x\) and \(\ln x\) because these functions are inverses.
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y/y (cos x) ln x + (sin x)/x Using the product rule and implicit differentiation. Differentiate implicitly with respect to x x and solve for dy dx. ln y (sin x) ln x taking the natural log of both sides. f ( x) and simplify using logarithm properties.
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