 Hello friends welcome to the session I am Malka let us discuss the question that is differentiate with respect to x the function in exercises 1 to 11 the given function is cos inverse x by 2 upon square root of 2x plus 7 where minus 2 is less than x is less than 2. So let us start with the solution y equal to cos inverse x by 2 upon square root of 2x plus 7. Now we differentiate question rule we get dy by dx equal to denominator that is 2x plus 7 into dy dx of numerator that is cos inverse x by 2 minus numerator which is cos inverse x by 2 into dy dx of denominator which is square root of 2x plus 7 upon denominator square that is 2x plus 7. We get dy by dx equal to square root of 2x plus 7 into dy dx of cos inverse x by 2 will be minus 1 upon square root of 1 minus x square by 4 into dy dx of x by 2 minus cos inverse x by 2 into dy dx of square root of 2x plus 7 will be 1 upon 2 into square root of 2x plus 7 into 2 upon 7 this implies dy by dx equal to minus 2x plus 7 into here on taking square root of 4 we get 2 so 2 will go in the numerator upon square root of 4 minus x square into 1 by 2 minus cos inverse x by 2 upon 2 to cancel out square root of 2x plus 7 upon x plus 7 this implies dy by dx equal to minus will be minus common this will give us here 2 to cancel out we get square root of 2x plus 7 upon square root of 4 minus x square plus cos inverse x by 2 upon square root of 2x plus 7 and in the denominator there it is 2x plus 7 we get dy by dx equal to now we take the same here we get 7 we get square root of 2x plus 7 into square root of 2x plus 7 plus cos inverse x by 2 into square root of 4 minus x square upon x plus 7 this implies dy by dx equal to minus common we get 2x plus 7 upon 2x plus 7 into square root of 4 minus x square into square root of 2x plus 7 plus cos inverse x by 2 into square root of 4 minus x square upon 2x plus 7 into square root of 4 minus x square into 2x plus 7 this implies dy by dx equal to 2x plus 7 will cancel out to 2x plus 7 we get minus 1 upon square root of 4 minus x square into square root of 2x plus 7 plus now we see that square root of 4 minus x square will cancel out to 4 minus square root of 4 minus x square we get cos inverse x by 2 upon 2x plus 7 into square root of 2x plus 7 therefore dy by dx equal to minus common 1 upon square root of 4 minus x square into square root of 2x plus 7 plus cos inverse x by 2 upon 2x plus 7 to the power 3 by 2 so hope you understood the solution I'll enjoy the session goodbye and take care