WebQuestion: Find the derivative of the function. f(x) = 3 ln(x)/ x^8. Find the derivative of the function. f(x) = 3 ln(x)/ x^8. Show transcribed image text. Expert Answer. Who are the … WebMay 24, 2015 · May 25, 2015 We can use the chain rule here, which states that dy dx = dy du du dx Thus, as it's not possible to directly derivate ln(x3), we can rename u = x3 and …
Worked example: Derivative of ln(√x) using the chain rule - Khan Academy
WebSolve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. WebJul 10, 2016 · Explanation: chain rule d du lnu = 1 u u = 3x, du dx = 3 d dx ln3x = 1 3x ⋅ 3 = 1 x Answer link Alexander Jul 10, 2016 Let y = ln(3x). Since d dx [ln(u)] = u' u, let u = 3x, so y' = 3 3x = 1 x In fact, we can generalize this formula even more if we notice that for any number a, and y = ln(ax), then y' = a ax = 1 x Answer link raymond beard
Derivative Of ln x, Natural Logarithm & More - Study Queries
Web3. what is the antiderivative of 2x 4. what is the antiderivative of f'(x) = 4x^3-3x^2+x-3 5. Draw ️if the statement is correct. Otherwise, draw a1. Antidifferentiation is the process … WebRelated Pages Natural Logarithm Logarithmic Functions Derivative Rules Calculus Lessons. Natural Log (ln) The Natural Log is the logarithm to the base e, where e is an irrational constant approximately equal to 2.718281828. The natural logarithm is usually written ln(x) or log e (x).. The natural log is the inverse function of the exponential function. WebThe derivative of the natural logarithm function is the reciprocal function. When f ( x) = ln ( x) The derivative of f (x) is: f ' ( x) = 1 / x Integral of natural logarithm (ln) function The integral of the natural logarithm function is given by: When f ( x) = ln ( x) The integral of f (x) is: ∫ f ( x) dx = ∫ ln ( x) dx = x ∙ (ln ( x) - 1) + C raymond beasley