MATH 1110H Midterm: MATH1110H-Test-Solutions
Document Summary
Simplify where you reasonably can: if you have a question, ask it, use the back sides of all the pages for rough work or extra space, you may use a calculator and (all sides of) an aid sheet. 1: compute dy dx for any four (4) of parts a f. 1 cos(x) ( sin(x)) = sin(x) cos(x) du dx ln(u)(cid:19) . 1 u d dx cos(x: chain rule again, with a bit of power rule; let w = x2, and then: dy dx d dx d dx tan(cid:0)x2(cid:1) = tan(w) = (cid:18) d. = sec2(cid:0)x2(cid:1) 2x = 2x sec2(cid:0)x2(cid:1) (cid:3) dw tan(w)(cid:19) dw dx. = sec2(w) d dx x2: chain rule with a bit of power rule again for the harder part; let w = x2, and then: dy dx d dx (cid:16)cos(x) + ex2(cid:17) = ew(cid:19) . = sin(x) + 2xex2 dw (cid:3) d dx dw dx cos(x) + d dx ex2.
