Techniques of Differentiation - Derivatives of Natural Logarithmic Functions
Techniques of Differentiation - Derivatives of Natural Logarithmic Functions
Find the derivative of each of the following w.r.t \(x\):
\(y = \ln{\left( (5x + 3)^2(3x^2 - 1) \right)} \)
\(y = \ln \left( \frac{7x^2 - 8}{2 - x} \right) \)
\( y = \ln { \left( (x + 3)(x - 2)^2(5 - 3x^2) \right) }\)
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Answer:(a) \(\displaystyle \frac{10}{5x+3}+\frac{6x}{3x^2-1}\). (b) \(\displaystyle \frac{14x}{7x^2-8}+\frac1{2-x}\). (c) \(\displaystyle \frac1{x+3}+\frac2{x-2}-\frac{6x}{5-3x^2}\).
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