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2. Calculating the Derivative of ln(x)^2 - Lesson | Study.com

   study.com/academy/lesson/calculating-the-derivative-of-ln-x-2.html

   For ln x 2, both positive and negative values of x are allowed because x is squared. The only constraint on x is that x ≠ 0. The function domain includes negative x. The derivative is the slope ...

3. How do you find the derivative of y=(lnx)^2? - Socratic

   socratic.org/questions/how-do-you-find-the-derivative-of-y-lnx-2-1

   1 Answer. Anjali G. Mar 19, 2017. dy dx = 2lnx x. Explanation: y = (lnx)2. Use the Chain Rule: dy dx = 2(lnx)(1 x) dy dx = 2lnx x.

4. General formula for the nth derivative of $ \ln(x^2 + x - 2 ...

   math.stackexchange.com/.../general-formula-for-the-nth-derivative-of-lnx2-x-2

   The corresponding expression is therefore: $$ b (n, k) = \frac {1} {2} [1 + (-1)^ {n+1}] + 2k $$. The exponents of $ x^2 + x - 2 $ in each term's denominator ($ c $) vary according to $ k $ (starting with $ k = 0 $) following the sequence of consecutive numbers which have their initial value determined by $ n $ according to the sequence {1, 1 ...

5. How do you differentiate y = lnx^2? - Socratic

   socratic.org/questions/how-do-you-differentiate-y-lnx-2

   Explanation: Just to show the versatility of calculus, we can solve this problem through implicit differentiation. Raise both side to the power of e. y = ln(x2) ey = eln(x2) ey = x2. Differentiate both sides with respect to x. The left side will require the chain rule. ey(dy dx) = 2x.

6. How do you find the derivative of #ln(ln x^2)#? - Socratic

   socratic.org/questions/how-do-you-find-the-derivative-of-ln-ln-x-2

   Explanation: We can use chain rule here. We can write f (x) = ln(lnx2) as. f (x) = ln(g(x)), g(x) = ln(h(x)) and h(x) = x2. then df dg = 1 g(x), dg dh = 1 h(x) and dg dh = 2x. and using chain rule as df dx = df dg × dg dh × dh dx. = 1 g(x) × 1 h(x) × 2x. = 1 lnx2 ⋅ 1 x2 ⋅ 2x. = 2 xlnx2.

7. How do you find the derivative of #y=ln (x^2+y^2)#? - Socratic

   socratic.org/questions/how-do-you-find-the-derivative-of-y-ln-x-2-y-2

   We have: y = ln(x^2+y^2) Method 1: Implicit differentiation, as is: Using the chain rule: dy/dx = 1/(x^2+y^2)(2x+2ydy/dx) " " = (2x)/(x^2+y^2) + (2y)/(x^2+y^2)dy/dx ...

8. How do you find the second derivative of (ln(x))^2? - Socratic

   socratic.org/questions/how-do-you-find-the-second-derivative-of-ln-x-2

   Explanation: As f (x) = (lnx)2. First derivative f '(x) = 2lnx × 1 x = 2lnx x. and second derivative can now be found using quotient rule. f ''(x) = x × 2 x −2lnx ×1 x2 = 2(1 − lnx) x2. Answer link.

9. calculus - What is the derivative of, $x e^{\ln(x^2)}$ -...

   math.stackexchange.com/questions/752807/what-is-the-derivative-of-x-e-lnx2

   Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

10. How do you find the derivative of #ln(x^2 +1)#? - Socratic

    socratic.org/questions/how-do-you-find-the-derivative-of-ln-x-2-1-1

    (2x)/(x^2+1) You have a composed function f(g(x)), where f(x)=ln(x), and g(x)=x^2+1 The rule for deriving composite functions is d/dx f(g(x)) = f'(g(x))*g'(x) which can be translated as "compute the derivative of the outer function with the inner function as argument, and multiply the derivative of the inner function". To complete our scheme, we need the derivatives: we have f(x)=ln(x ...

11. What is the derivative of lnx/x^2? - Socratic

    socratic.org/questions/what-is-the-derivative-of-lnx-x-2

    1 Answer. use the quotient rule, which should be memorised. f (x) = u v ⇒ f '(x) = vu' −uv' v2. f (x) = lnx x2. u = lnx ⇒ u' = 1 x. v = x2 ⇒ v' = 2x. f '(x) = x2 × 1 x − 2xlnx (x2)2. f '(x) = x −2xlnx x4 = x(1 −2lnx) x4 = x(1 − lnx2) x4 x3.