Please help me with the following questions. Thanks in advance.

QUESTION 1 tan ( 5x) Use the Quotient Rule to find f '(x) given f (x) = x2 + 7 For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). B I US Paragraph Arial V 10pt PQUESTION 2 This problem has two parts. Please clearly show you work each part and clearly label the answers for each part. Answers without work will receive credit. a) Use implicit differentiation to find . x3+y = 3xy dx b) Find an equation for the tangent line to the function above at the point For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).QUESTION 3 Find the derivative using the limit definition of the derivative. (Using difference quotient) Show your work and clearly label your answers. Answers that do not show work will not receive credit. y =3x2- 5r + 2 For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). B I U S Paragraph ArialQUESTION 4 Show your work. Clearly number and label your answers. Answers without any work will not receive any credit. dy Find . y = 2r cost For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).QUESTION 5 Show your work. Clearly number and label your answers. Answers without any work will not receive any credit. x2-4r - 21 Find the limit. Show all work. lim 1-7 x -49 For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BIUS Paragraph V Arial 10ptQUESTION 6 Show your work. Clearly number and label your answers. Answers without any work will not receive any credit. dy Find y = In(sec x) dx For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BIUS Paragraph y Arial 10ptQUESTION 7 Show your work. Clearly number and label your answers. Answers without any work will not receive any credit. Find f(x). f(x) = csc -(4x) For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BIUS Paragraph Arial 10pt HQUESTION 8 Show your work. Clearly number and label your answers. Answers without any work will not receive any credit. Find the second derivative. f (x) =\\ 3x - 2 For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). B IUS Paragraph Arial 10ptQUESTION 9 Show your work. Clearly number and label your answers. Answers without any work will not receive any credit For this problem there are multiple parts and multiple answers required and all the required responses for each part in your written work. Given the function / (x) =x4- 12x3 8) Find all critical points, and list as ordered pairs. (Show work) bj Determine the intervals where the function is increasing and the intervals where the function is decreasing, use interval notation Use the first derivative fest to find any local minimums or local maximums. Please list as ordered pairs, (x y) (Show work ) increasing decreasing local minimums: local maximums. c) Determine the intervals where the function is concave down, concave up and find any inflection points. (2nd Derivative) (Show work ) concave up concave down inflection points: For the toolbar. press ALT-F10 (PC) or ALT+FN+F10 [Mack B I Y S Paragraph Arial 10pt I.QUESTION 10 Related Rates: A cylyndrical ice sculpture is melting at a rate of 4 fto /min, but the height always remains 3 times the diameter. Find how fast the height is shrinking when the cylinder is 10 ft. tall. Use Volume V=arth Please leave in exact form, not decimal approximations. diameter r h For the toolbar. press ALT+F10 (PC] or ALT+FN+F10 (Mac). B / U S Paragraph Arial 10pt EVEAVQUESTION 11 Show your work and clearly label and number your answers. Answers without supporting work will not receive any credit. Use L'Hopital's Rule to find the limit. Show that it is appropriate to use. sinx - x lim r+0 xsir For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BIUS Paragraph Arial 10pt vQUESTION 12 Find the antiderivative. 2 5x + + 1 dx 3.x- For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BIUS Paragraph V Arial 10pt V V P O WORDS POWERED BY TIN