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Home » Find the derivative of \( y = \ln(x^2 + 1) \) at \( x = 1 \). - AMAZONAWS

Find the derivative of \( y = \ln(x^2 + 1) \) at \( x = 1 \). - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Ein Materialwissenschaftler untersucht die Wärmeleitfähigkeit \( k \) eines Verbundwerkstoffs mit der Regelung \( k = \frac{k_1 k_2 d_1 + k_2 d_2^2}{d_1 + d_2} \), wobei \( k_1 = 200 \) W/m·K, \( k_2 = 50 \) W/m·K, \( d_1 = 2 \) m und \( d_2 = 1 \) m. Wie groß ist \( k \)?

📌 Berechne \( k_1 d_1 = 200 \times 2 = 400 \).

📌 Berechne \( k_2 d_2^2 = 50 \times 1^2 = 50 \).

📌 Zähler: \( 400 + 50 = 450 \).

📌 Nenner: \( 2 + 1 = 3 \).

📌 Also \( k = \frac{450}{3} = 150 \) W/m·K.

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📌 Ein Robotikingenieur entwirft einen Differentialantrieb, bei dem der Winkel \( \theta \) des Rades mit der linearen Geschwindigkeit \( v \) durch \( v = \, v_r (r_L + r_R \cos\theta) \) zusammenhängt, wobei \( v_r = 0.5 \) m/s, \( r_L = 0.2 \) m, \( r_R = 0.1 \) m und \( v = 0.6 \) m/s. Wie groß ist \( \theta \) in Radiant?

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