WebExample 1: Find the derivative of ln (2x - 3). Solution: Let f (x) = ln (2x- 3). We know that the derivative of natural log is 1/x. Using this and chain rule, we get f' (x) = 1/ (2x - 3) · d/dx (2x - 3) = 1/ (2x - 3) · (2 - 0) = 2 / (2x - 3). Answer: The derivative of the given function is 2 / (2x - 3). Example 2: Find the derivative of ln x 2. WebCalculus 2 Midterm Quiz 2 by bOn 8/10 Score Attempt 3 Question 1. Complete Mark 1 out of 1. Flag question. Question text. Functions as x approaches plus or minus infinity
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WebJan 25, 2016 · Explanation: Here I would use the Chain Rule applied to your function: f (x) = ln(cos(2x)) deriving ln as it is, multiplying by the derivative of cos as it is (red) and finally multiplying by the derivative of 2x (blue): f '(x) = 1 cos(2x) ⋅ −sin(2x) ⋅ 2 = − 2 sin(2x) cos(2x) = −2tan(2x) Answer link WebSolution to Example 3. Let u = x2 + 2x − 1 and f(u) = √u which give du dx = 2x + 2 and df du = 1 2√u Use the chain rule we obtain f ′ (x) = df du du dx = 1 2√u(2x + 2) Substitute u = x2 + 2x − 1 above to obtain f ′ (x) = 2x + 2 2√x2 + 2x − 1 … great clips oviedo check in
What is the derivative of? : d/dx cos(ax) Socratic
WebFind the Derivative - d/dx (sin (x)) (cos (x)) (sin(x))(cos (x)) ( sin ( x)) ( cos ( x)) Differentiate using the Product Rule which states that d dx[f (x)g(x)] d d x [ f ( x) g ( x)] is f (x) d dx[g(x)]+g(x) d dx [f (x)] f ( x) d d x [ g ( x)] + g ( x) d d x [ f ( x)] where f (x) = sin(x) f ( x) = sin ( x) and g(x) = cos(x) g ( x) = cos ( x). WebThis is about Engineering Mathematics. Hope it will help you. chapter differentiation introduction of derivative rules for differentiation higher order WebObtain the first derivative of the function f (x) = sinx/x using Richardson's extrapolation with h = 0.2 at point x= 0.6, in addition to obtaining the first derivative with the 5-point formula, as well as the second derivative with the formula of your choice . great clips oviedo