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MTH 261-A Test unit ! | Ench part of each problem Counds 7pts. 1. Find the...
11. (5 points each) Find the derivative of each function. DO NOT simplify your answers. cos(x) a) f(x) = 1-tan(x) b) f(x) – tan-" (4x²) dy 12. Consider the equation x² + xy + y² = 1. Find an expression for by implicit differentiation. dx
dy For the following composite function, find an inner function u = g(x) and an outer function y=f(u) such that y=f(g(x)). Then calculate dx y=tan (2x) Calculate the derivative of the following function. y = (5x - 19) dy Carry out the following steps for the given curve. dy a. Use implicit differentiation to find dx b. Find the slope of the curve at the given point. x +y = 337;( - 4,3) a. Use implicit differentiation to find b....
ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y = f'(x) (c) state the domain of f and the domain of f. Find lin tan 4x cos 3x sin 5x X> 12 Find y if y = (3x+5)*(x+4x) (3 Find y' it ya + 10x tanx 7 Let y= (a) Find (6) Find the equation of the tangent line at (74 y' Elf 8 X3 Prove lim (5-) = 4 (a) write the...
2. (each 1 mark) Find the derivative of the following functions: 9x + 7 (a) y = 92 - 1 (b)r = (02 9016 /09 - 9 ( 9 ) (c) y=rºcot x + 9x2 cos x – 14x sin x 9t sint (d) s = cost + +9 (e) h(x) = cº sin (vą) + 240 sec (1) ) 10 (f) f(0) = (_sin 98 (1+cos 90 ) (g) g(x) = (1 + csc(+10) + In (922 – 8)...
1. (6pts) Find the domain of f(x) = x+6 V17+ 2x 2. (7pts) Given f(x) = Vx-4, (a) write out the conjugate of f(x+h)-f(x). f(x+h)-f(x) (b) use the conjugate to simplify completely
Find the derivative and do not simplify. I will thumbs up if anyone can help (1-4x)3 d) y = In (3x+2)5 e) y = ( 5x – sin3x)8 f) y = log. (x csc x) g) y = x 5x
1. Find the slope for each of the functions below: (a) y = f(x) = 52 (b) y = f(x) = 1 3 x 3 + x 2 + 4x − 10 (c) y = f(x) = 1 3 x 3 + x 2 + 4x + 400 (d) y = f(x) = x 1 2 (e) = f(x) = 4x 1 2 + x 2 − .1x 3 − 5 (f) = f(x) = 4x + 6 (g) y...
Using the definition, calculate the derivative of the function. Then find the values of the derivative as specified. f(x) = 3 + x2: f'(- 9), F 'O), f (9) Using the definition, calculate the derivative of the function. Then find the values of the derivative as specified. 4 96) = 3. g'(-2), g'(4), g(6) o't)= dx if y = 7x3 dy || s={3 - 4+, t= -6 s'(t)= 0 ne indig y=f(x)= 3 + 14-x, (x,y)= (0,5) The derivative of...
1. Find and simplify the derivative of each of the following functions: In(2 1) 2x 1) tan 1In(tan) (a) (x)In (b) f(x) = (412-1)3 In(4z?-1) (g) f(r)-n (n) f(x) = ln(sec 3r-tan 3r) 1 +x ln a
3x+2 f(x) =( :) (x-> +1) Your problem: using the rules of differentiation, find the derivatives of the collowing: f)-(3442) fool(3x+2) (-5x + x + 1) - 2 1 =(-15x 10x" + (-2x = 2) =>15x410x5 - 2x = = 3x -3x- 27 (X)(3+0)-(3x+2)(1) x² g'=(x) =F12x15x4_2 = -5x6 xb * please check my work, if wrong, please write out correct solation! Chain Rule: When functions are composed, to take the derivative involves both the outside function and the inside...