Find the derivative of the function. See Examples 1, 2, 3, and 4. y = In(8...
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...
at the point (2, -3). Give an 4. Find the minimum value of the directional derivative of the function f(x, y)- exact answer. 2.
at the point (2, -3). Give an 4. Find the minimum value of the directional derivative of the function f(x, y)- exact answer. 2.
Find the derivative of the function y= 4 In 3x 2 + 5x 4(2 + 5x -5 In (3x)) y': x(2 + 5x)2
1. Find the derivative of the function y (x) , showing all steps used 2. Find the derivative of the function y(x)In x), showing all steps used. 3. Show that sin(x) 1- (sin(x) cot (x))2, showing all steps 4. Evaluate the following integral:珓 1-cos' (x) cos(x) dx, showing all steps. 5. If the rate at which a car's position is changing is given by the formula0.3t2 - 2.0t +100, where x is in meters and t is in seconds, find...
Find the derivative of the function. y = log 4 V7x + 8 7 O A. In 4 OB. 7 In 4 (7x+8) O c. 7 2( In 4)(7x+8) OD. 7 In 4 7x + 8
uestion 2 Find the derivative of the function. y = (x + 1)2(x 2 + 1)-3 -2x + 1x2x2 + 3x - 1) (x2 +14 2(x + 1x2x2 – 3x - 1) (x2 +14 -2(x+1x2x2 – 3x - 1) (x2 +14 2(x + 1x2x2 + 3x - 1)
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...
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. g(x) = 800(3 - e-0.1x) Find the derivative of the function. y = :ets Find the derivative of the function. y = 4e(x2 + 6)3 Find the derivative of the function. y = In(e2x + 3)
1. Find the directional derivative of the function f(x, y, z) = 2.cy – yz at the point (1,-1,1) in the direction of ū= (1,2,3). Is there a direction û in which f(x, y, z) has a directional derivative Dof = -3 at the point (1,-1,1)?