 Hi, and welcome to the session. Let's discuss the following question. The question says, using differential, find the approximate value of the following. First part is 17 by 81 to the power 1 by 4. Let's now begin with the solution. We will consider the function i equals to fx equals to x to the power 1 by 4. And let x is equal to 16 by 81 x plus delta x is equal to 17 by 81. From this, we can say that delta x is equal to 17 by 81 minus 16 by 81. This implies delta x is equal to 1 by 81. We know that if y is a function of x and there's a x as a small change in x, then corresponding to this change, there is a corresponding change in y also, which is denoted by delta y. Thus, y plus delta y is equal to f of x plus delta x. Now this implies y plus delta y is equal to x plus delta x to the power 1 by 4. This implies delta y is equal to x plus delta x to the power 1 by 4 minus y. This implies delta y is equal to x plus delta x whole to the power 1 by 4 minus x to the power 1 by 4. And this is equal to x plus delta x is 17 by 81. This is equal to 17 by 81 whole to the power 1 by 4 minus 16 by 81 whole to the power 1 by 4. This is equal to 17 by 81 whole to the power 1 by 4 minus 2 by 3 to the power 4 whole to the power 1 by 4. And this is equal to 17 by 81 whole to the power 1 by 4 minus 2 by 3. So delta y is equal to 17 by 81 to the power 1 by 4 minus 2 by 3. And this implies 17 by 81 to the power 1 by 4 is equal to delta y plus 2 by 3. Now delta y is equal to dy by dx into delta x plus 2 by 3. Now y is equal to x to the power 1 by 4. And this implies dy by dx is equal to 1 by 4 into x to the power minus 3 by 4. So this is equal to 1 by 4 into x to the power minus 3 by 4 into delta x is 1 by 81. So we have 1 by 81 plus 2 by 3. Now this implies 17 by 81 whole to the power 1 by 4 is equal to 1 by 4 into x to the power 3 by 4 into 1 by 81 plus 2 by 3. This is equal to 1 by 4 into, we will substitute the value of x which is 16 by 81 to the power 3 by 4 into 1 by 81 plus 2 by 3. This is equal to 1 by 4 into 2 by 3 to the power 4 whole to the power 3 by 4 into 1 by 81 plus 2 by 3. This is equal to 1 by 4 into 2 by 3 whole q into 1 by 81 plus 2 by 3. This is equal to 3q divided by 4 into 2q into 1 by 81 plus 2 by 3 is equal to 27 divided by 4 into 8 into 1 by 81 plus 2 by 3. On simplifying this, we get 1 by 96 plus 2 by 3, this is equal to 1 plus 32 into 2 divided by 96 and this is equal to 65 by 96, on simplifying this, we get 0.677, hence our required answer is 0.677. So this completes the session by and take care.