MATH 1131Q Lecture 6: Derivative of Trig Functions, Chain Rule

560 Test exercise 7 Write out the solutions carefully. They all quite straightforward. 1 Differentiate the following with respect to x: 38 (b) (Sr +3,- (O cosh, (a) tan 2x sin, 4x er)-3x 2 lfx2 + ,2-2x+2y-23,find/rand얽at the point where x--zy. 4 Ifx-11-cos" and y-3(.-sin") find a and a: in their simple (d) kg.dr.3x-1) sina 田 (x+1 diy when r,y,4ay2以 3 Find an expression for forms Further problems 7 39 1 Differentiate with respect to (b) In(secx+tanx (c) sinxcos'x 2 Find when: a)y-14 cosx if y is a function of x, and x-T+1 show that훑-x(1-x)dr 3 5 Differentiate coshx-1 coshx1 ",.tow. "r-wrmF} o, ,.刍 7 If(x-n'-A(x + y. prove that (2x + y -x+2y. If.e + 2xy + 3,-이.prove that (x + 3 '헒+2tx2 + 2xy + 9 Scanned by CamScanner

3. a) Find vector v from point (e, -e-e) to the point (3e,e,e) b) Find parametric equations for the line l,through (T, T, t) in the direction of vector v c) Does the line l pass through the origin (contain the point (0,0,0))? Explain your reasoning d) Use a computer algebra system to produce a picture of the line, the vector v and the points: e, -e, -e), (3e, e, e), Tu,T), C0,0,0).

→ (1 point) Let F = xit(x + y) + (x-y+1) k. Let the line l be x = 51-3, y =-(4+4), z = 2 + 4. (a) Find a point P = (x0,yo,zo) where F is parallel to l. Find a point Q = (xi , yi , a) at which F and I are perpendicular Q= Give an equation for the set of all points at which F and I are perpendicular. equation: