Using the Chain rule find the derivative of the function: 1. y=(2x²-3x+1)10
Using the Chain rule find the derivative of the function: 1. y=(x?+2x2,6
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...
find the derivative Find the derivative of the function. y=9 eX + e 2x dy dx Find the derivative of the function. y=9 eX + e 2x dy dx
Find the derivative of y with respect to x. y= In 1 + 2x X2 OA. -4-3x 2x OB. 4 – 3 x 2x(1 + xx) -4-3/ 2(1+) -4-377 2x(1+x) OD.
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 so we must use the Chain Rule, given below, to find the derivative dx[f(g(x))) = f '(g(x))g'(x) For the given function sin 1(5x+ 1), the "inside" function is Sx + and the foutside" function is arcsin (a) Part 2 of 3 Recall that the derivative of y sin-1(x) is 1-(5x - 1)2 Find the derivative of...
72 6) Find the derivative of f [2 - (2x + 1) using the product rule. a) 0 2 + + 1 b) 4 + 1 c) O 2 - 1 х d) - 2
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
8. Using Chain Power Rule a) ∫ (3X^2 + 4)^5(6X) dx b) ∫](2X+3)^1/2] 2dx c) ∫X^3](5X^4+11)^9 dx d ∫(5X^2(X^3-4)^1/2 dx e) ∫(2X^2-4X)^2(X-1) dx f) ∫(X^2-1)/(X^3-3X)^3 dx g) ∫(X^3+9)^3(3X^2) dx h) ∫[X^2-4X]/[X^3-6X^2+2]^1/2 dx
1120 Page 1 of 1. Find the derivative of the function y = + + x2 using (a) the quotient rule (b) the product rule (without using the quotient rule) (c) the power rule (without using the product rule or quotient rule) For cach, clearly show and/or explain how to use the respective rule to find the derivative. (d) Which method, (a), (b), or (e), do you think is best for finding this derivative? Why?
4 In 2x Find the derivative of the function y= 4 + 5x · y 777