**Problem Statement:** Differentiate the following expression: \[ y = x^{\ln x} \] **Options:** - \( \frac{2 \ln x}{x} \) - \( x^{\ln x} - 1 \ln x \) - \( (\ln x)^2 \) - \( 2x^{\ln x} - 1 \ln x \) *(Selected option)* **Explanation:** You are given a mathematical function involving an exponent with a variable base raised to the power of a logarithmic function. The task is to differentiate this expression with respect to \( x \). Use appropriate differentiation techniques, such as logarithmic differentiation, to solve the problem accurately. Explore each option to verify the correct derivative of the given function.

Q: 1/3y-9=1/10y

A: Here given as 13y-9=110y Here y is not equal to 0 and 3.

Q: Let à = (2, 3, 4) and b = ( − 2, 0, — 5). Find à x 6.

A: A detailed solution is given below

Q: 8 - 128x V81 - 64x2 "xp-

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Q: Let A= [4,7] and B= (1,5) find the following a. A U B b. A n B c. B-A d. A n B^c

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Q: Tow19w²+ low =0

A: Given equation is It can be written as Now, we factorize the quadratic polynomial by splitting…

Q: -4.-3-2=1./7i ż 3 나 4.4014)unt write the domain -and range.of. h. Using

A: Given query is to find the domain and range of the graph.

Q: The central difference has the same value as the average of the forward and backward difference. O…

A: Forward difference f'x=fx+h-fxh Backward Difference f'x=fx-fx-hh Central Difference f'x=fx+h-fx-h2h…

Q: Evaluate xe2+ dx. *xP x

A:

Q: 1. 2y"" Hardcore 0 7y"+12y + 8y

A: To solve the given differential equation.2y'''-7y''+12y'+8y=0

Q: 1/3y+4=1/5y

A:

Q: Let a = (-1,0, 5) and 6 = (3,-1,0). Find à x 6. < V

A:

Q: Find the value lf x that makes DEF XYZ

A: Two triangles are said to be similar if their corresponding angles are congruent and the…

Q: 7. A cannonball is fired from a cannon at the edge of a hill. See the figure below: Vo = 20 m/sec is…

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