Calculate the derivative of z11y + yºz + xzº = 12 using implicit differentiation. (Use symbolic...
Find the derivative of the function y = 3e (In (82) (Use symbolic notation and fractions where needed.)
Use the Quotient Rule to calculate the following derivative for f(x) = 1x + x (Use symbolic notation and fractions where needed.)
9. Derive the formula for the derivative of arctan x. Hint: Use implicit differentiation on y = arctanx, draw a right triangle with y as the angle.
Find the derivative using the appropriate rule or combination of rules. y = (kx + b)-1/3 where k and b are any constants. (Use symbolic notation and fractions where needed.) y' =
Use the Chain Rule to evaluate the partial derivative at the point (r,0) = (2v2, 4), where g(x, y) = x+, x = 32r cos(o), y = 3r sin(0) (Use symbolic notation and fractions where needed.)
evaluate without using a calculator. sin^-1(sin(-17pi/6)) (1 point) Evaluate without using a calculator. (Use symbolic notation and fractions where needed.) sin-' [sin(174) ) = 0 help (fractions)
Find the definite integral using Part 2 of the Fundamental Theorem of Calculus. (Use symbolic notation and fractions where needed.) L' avem dy = 0
Find the solution of dy/dt=2y(3−y), y(0)=9. (Express numbers in exact form. Use symbolic notation and fractions where needed.)
Use implicit differentiation to find y' and evaluate y'at (-1,-6). 9xy + y-48 = 0 y' = Evaluate y' at (-1,-6). y'l(-1,-6)=0 (Simplify your answer.) Find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema. f(x) = x + 10x + 21 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The function is increasing on (Type your answer using interval...
⒈ Consider the equation x2y2=c, where c is a real constant.(a) Assuming that this implicitly defines a differentiable function y=f(x), use implicit differentiation to find an expression for dy/dx.(b) For what combination of x and c is your answer to Part (a) valid?(c) Assuming c>0, find all of the possible functions f and verify that the derivative f' satisfies the expression found in Part (a).