3. (8 points each) Find the derivative of each function. Show as much work as possible....
Differentiate the function ??(??) = ??4 ln(5??) + ln ( 3??+2 2??−3 ) 3x+2 Differentiate the function f(x) = x4 ln(5x) + In 2x-3 For full credit show each step. You do not need to simplify the answer. (10 points)
8. [0/5 Points] DETAILS PREVIOUS ANSWERS Find the derivative of the function. f(t) = 43/2 log&(vt + 3) 1 3x?loge (Vx+3) 3 2 f'(t) = X + 2 2 ln(6)(x+3) x
4. (a) (5 points) Find the derivative of the function sin(x² +1). f(x)= Vx+1 (b) (5 points) Find the derivative of the function g(x) = ln(1 - 0);
4. (a) (5 points) Find the derivative of the function f(x) sin(22 +1). Vx+1 (b) (5 points) Find the derivative of the function g(x) = ln(1 – x); (c) EXTRA CREDIT (5 points): Find a formula for g(n)(x) (the nth derivative of g(x)), n> 1, where g(x) is as in (b). (Recall that n! = = n(n − 1)(n − 2)...3.2.1).
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
1. (-/1 Points] DETAILS BERRAPCALCBR7 2.4.005. Find the derivative of the function by using the Product Rule. Simplify your answer. f(x) = x (x + 1) F"(x) = Submit Answer 2. [-/1 Points] DETAILS BERRAPCALCBR7 2.4.017. Find the derivative of the function by using the Product Rule. Simplify your answer. F(X) = (7x + 4)(1 = x) f'(x) = 3. [-/1 Points) DETAILS BERRAPCALCBR7 2.4.035. Find the derivative of the function by using the Quotient Rule. Simplify your answer. f(x)...
1. Find the derivative of each function and simplify your final answer. SHOW WORK (x)-(xx (2-3x2 x2 +1 B) g-1 x2-1 1. Find the derivative of each function and simplify your final answer. SHOW WORK (x)-(xx (2-3x2 x2 +1 B) g-1 x2-1
Find the second derivative of the function. y 4(x2 2x)3 24x2(1 x)(2+x) X y" = Need Help? Read It Watch It Talk to a Tutor 0/1 points | Previous Answers LarApCalc10 2.6.014. 1/100 Submissions Used My Notes Ask Your Find the third derivative of the function. f(x) x4-4x3 3)(x2 + 3x )2 (x)12(2r X Need Help? Read It Watch It Talk to a Tutor 1/1 points Ask Your 6. Previous Answers LarApCalc10 2.6.016. 1/100 Submissions Used My Notes Find the...
vements, choose Check for Updates For maximum credit, show all work! 1. Find each of the following limits If it exists. lim f(x) where f(x)-2-1 x d) is the function f of part c) continuous atx=4? Explain. e) lim 2. Find the derivative of each of the following. Use shortcut rules. You do not need to simplify: a) y = 3x2 +5 b) = (2x +5x72/x - 3) 10le? +16) MacBook Air
3. (a) (3 points) Write the definition of the derivative of a differentiable function f(x) at = a; (b) (7 points) using the definition of derivative as in (a), find the derivative of the function f(x) = Vx at a = 2. (c) EXTRA CREDIT (2 points): State the MEAN VALUE THEOREM (you can also draw a picture) and give its PHYSICAL interpretation in terms of INSTANTANEOUS and AV- ERAGE VELOCITIES.