3. (8 points each) Find the derivative of each function. Show as much work as possible....
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
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)
Please show all work! :) Find the derivative using any method. You don't need to simplify. a. (2 points) f(x) = 2x11 – 17 + b. (3 points) f(x) = x2 tan-1 x c. (3 points) f(x) = d. (2 points) f(x) = ln(33 – 7x)
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
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.
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
3. (5 pts) For each of the listed functions, determine a formula for the derivative function. For the first two, determine the formula for the derivative by thinking about the nature of the given function and its slope at various points; do not use the limit definition. For the latter three, use the limit definition, Pay careful attention to the function names and independent variables. It is important to be comfortable with using letters other than f and r. For...
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