1. ## Differentiate the following Trigonometric function(check my answers)

1)$\displaystyle y=sin(2x+5)$
$\displaystyle =2cos(2x+5)$
2)$\displaystyle y=sec\sqrt{x}$
$\displaystyle =\frac{sec\sqrt{x}tan\sqrt{x}}{\sqrt{x}}$
3)$\displaystyle y=cosxsin3x$
$\displaystyle =3(cosx)(cos3x)-(sin3x)(sinx)$
4)$\displaystyle y=2sec2x-csc^2 3x$
$\displaystyle =4sec2x tan2x+6csc^2 3xcot3x$
5)$\displaystyle y=cos^2 (4x^5 +1)$
$\displaystyle =-2(cos4x^5 +1)(sin4x^5)(20x^4)$

Please check is my answers are correct, and if there arent please try to solve them in steps...
Thank you

2. Originally Posted by mj.alawami
1)$\displaystyle y=sin(2x+5)$
$\displaystyle =2cos(2x+5)$
2)$\displaystyle y=sec\sqrt{x}$
$\displaystyle =\frac{sec\sqrt{x}tan\sqrt{x}}{{\color{red}2}\sqrt {x}}$
3)$\displaystyle y=cosxsin3x$
$\displaystyle =3(cosx)(cos3x)-(sin3x)(sinx)$
4)$\displaystyle y=2sec2x-csc^2 3x$
$\displaystyle =4sec2x tan2x+6csc^2 3xcot3x$
5)$\displaystyle y=cos^2 (4x^5 +1)$
$\displaystyle =-2(cos4x^5 +1)(sin4x^5{\color{red}+1})(20x^4)$

Please check is my answers are correct, and if there arent please try to solve them in steps...
Thank you
See above