Find the derivative of the function. y sin-1(5x+ 1) Part 1 of 3 The function y - sin-1(5x + 1) is a composition, and...
Q2 a) Find the second derivative of the following function y = tan x + sin-1x b) Using chain rule find any as function of y for the following function y = Vē – 1, x = t2 In x c) Using L'Hopital's rule find the limits as x approach 1 of the function d) find for the function y = ln xy + log10 (x + 3) + 2*+sinh-1x dx
Find the derivative of the function. y=5 e 2x2-3 dy 80 e 2x2x2 * + 20 e 2x2 X X Try again. Differentiate the exponential using the Chain Rule. to le 9(x) = g(x)g'(x) OK Find the derivative of the given function. y = (3x2 + 5x) -7x e -7x -7x y' = -21 e -7xx2 -29 +5e (Type an exact answer.) x X That's incorrect. The product rule states that if f(x) = u(x)•v(x), and if both u'(x) and...
Provide an appropriate response. Find the second derivative of the the function y-sin-12x och 1 - 4x2 2(1 - 4x2,32 (1 - 4x2,312 "-4392 Find any 5**v = yn In 5 In y 5x + y -5x + y + in 5-1 5x + y 5x + V + In 5 vin 5 - 1 vin 5-1 Find the derivative of y with respect to x, t, or, as appropriate.y = 4+2ee dee Use l'Hopital's Rule to evaluate the limit....
In the previous question we used the chain rule to calculate the derivative fog indirectly from the derivatives off and g. Of course, in the previous question f and g were polynomials, and so a simpler method to find the derivative would be to first evaluate f g and then differentiate. However, this "simpler" method does not always work. For example, use the chain rule f(8(x)) = f'(8(x))g'(x) to evaluate: di sin(x3 +1) = d e(x3+1) -1) = datan-1(x3 +...
-/1 POINTS SCALC8 2.5.045. Find the derivative of the function. y = cos( V sin(tan(5x)))
1.2. If w =exp(x+y) and x = sin(311) and y = 21cos(-131), find w/ot in two ways, once by plugging in, and once by the chain rule. 3. Show why it is true that, if f(x, y) = implicitly defines y as a function of x. we can compute the derivative dy/dx as the negative of the quotient of f/ox and 51/by. 4. Find the directional derivative of the function f(x.y) = (x+1)* cos(-3)) at the point (0.1) in in...
4. g(t)= 3. y=sin(tan5x) In problems 1-5, find the derivative of the function. Write your answers in simplest form. 1. f(x)=- sinx 2. f(x)=(x +7x-2) 100 1-COS X 3. y =sin(tan5x) 4. g(t)= t+3 5. f(x) = cos(x'cscx) sin(x-3) 6. Find lim 2-3 3x-x?
Find the derivative of the function. F(x) = x – 5x V x √x (a) Simplify the function to the point where you will not need the Product or Quotient Rule (b) Use the part a), find the derivative of the function. F'(x) =
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...
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...