Section 3.8 Derivatives PDF
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This document contains a collection of calculus problems involving logarithmic differentiation. It includes various derivative calculations emphasizing the logarithmic differentiation technique. The problems demonstrate applications of this method.
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3.8 3 𝑑𝑑𝑑𝑑 1) 𝑦𝑦 = ln (𝑡𝑡 2 ) Find. 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 2) 𝑦𝑦 = ln (ln(ln 𝑥𝑥)) Find. 𝑑𝑑𝑑𝑑 1 1−𝑥𝑥 𝑑𝑑𝑑𝑑 3...
3.8 3 𝑑𝑑𝑑𝑑 1) 𝑦𝑦 = ln (𝑡𝑡 2 ) Find. 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 2) 𝑦𝑦 = ln (ln(ln 𝑥𝑥)) Find. 𝑑𝑑𝑑𝑑 1 1−𝑥𝑥 𝑑𝑑𝑑𝑑 3) 𝑦𝑦 = ln Find. 2 1+𝑥𝑥 𝑑𝑑𝑑𝑑 4) Find the derivative of y = log 7 √2𝑥𝑥 − 3. Hint rewrite log7 in terms of ln. Recall 𝑑𝑑𝑑𝑑 5) Find of y = 5x. Hint rewrite 5x as e to some power. 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 4 6) Find of y = 2𝑥𝑥. 𝑑𝑑𝑑𝑑 Logarithmic Differentiation – derivatives of positive functions given by formulas that involve products, quotients and powers can be found more quickly with this technique. 1. Take the natural logarithm of both sides, and rewrite using the product, quotient, and/or power rule of logarithms. 2. Then differentiate. 𝑑𝑑𝑑𝑑 7) 𝑦𝑦 = tan 𝜃𝜃 √2𝜃𝜃 + 1 use logarithmic differentiation to find. 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 8) 𝑦𝑦 = 𝑥𝑥 (𝑥𝑥+1) use logarithmic differentiation to find. 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 9) 𝑦𝑦 = 𝑥𝑥 sin 𝑥𝑥 use logarithmic differentiation to find. 𝑑𝑑𝑑𝑑
