First Off, I Can't Hardly See The Functions, SO if a NUMBER is off by a tad, it's because I couldn't see it from the photo. Some answers, have been simplified...
A. Product Rule
[tex]f(x) = {x}^{5} \sin(5x) \\ f'(x) = ( {x}^{5} \times 5 \cos(5x) ) + ( {5x}^{4} \times \sin(5x)) \\ f'(x) = {5x}^{4} (x \cos(5x) + \sin(5x) ) [/tex]
B. Chain Rule
[tex]f(x) = (x + \sin(x))^{23} \\ f'(x) = 23(x + \sin(x)) ^{22} (1 + \cos(x))[/tex]
C. I CAN'T READ THIS ONE FROM THE PHOTO
D. Quotient Rule
[tex]f(x) = \frac{3 + \frac{3}{x} }{3 - \frac{3}{x} } \\ f'(x) = \frac{((3 - \frac{3}{x} ) \times ( \frac{ - 3}{ {x}^{2} } )) - ((3 + \frac{3}{x} ) \times ( \frac{3}{ {x}^{2} } ))}{(3 - \frac{3}{x}) ^{2} } [/tex]
