[গণিত] হলে, [গণিত] এর মান কোনটি ?
ক. [গণিত]
খ. [গণিত]
গ. [গণিত]
ঘ. [গণিত]
উত্তর: [গণিত]
ব্যাখ্যা: [গণিত] find the derivative dxdy of the function y= [গণিত] −1(1−9x26x), we can use a trigonometric substitution [গণিত] simplify the expression before differentiating. Let 3x= [গণিত] . Then x=31tan [গণিত] , which means [গণিত] = [গণিত] −1(3x). Substituting 3x= [গণিত] into the function: y= [গণিত] −1(1−(3x)22(3x)) y= [গণিত] −1(1− [গণিত] 2 [গণিত] 2tan [গণিত] ) We know the double angle identity for tangent: [গণিত] (2 [গণিত] )=1− [গণিত] 2 [গণিত] 2tan [গণিত] . So, the expression simplifies [গণিত] : y= [গণিত] −1( [গণিত] (2 [গণিত] )) y=2 [গণিত] Now, substitute [গণিত] = [গণিত] −1(3x) back into the equation: y=2tan−1(3x) [গণিত] find dxdy, we differentiate with respect [গণিত] x: [গণিত] Using the chain rule, we have: [গণিত] So, the value of dxdy is 1+9x26.
HSC Higher Math 1st Paper Chapter 9: অন্তরীকরণ MCQ — Prosthuti প্রশ্নব্যাংক
HSC · Higher Math 1st Paper · Chapter 9: অন্তরীকরণ · MCQ