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)
1. Find Derivative: y=2x^3 ln(2x^3+7) a. y' = 36x^4 ÷ 2x^3+7 b. y'=12x^5 ÷ 2x^3+7 - 6x^2 ln (2x^3+7) c. y' = -36x^4 ÷ 2x^3 +7 d. y'=12x^5 ÷ 2x^3+7 + 6x^2 ln (2x^3+7) e. y'=2x^3 ÷ 2x^3+7 - 6x^2 ln (2x^3+7) f. 2x^3 ÷ 2x^3+7 + 6x^2 ln (2x^3+7) 2. Find exact value of the expression. Sin(arctan(x/4)) a. √16-x^2 ÷ x. b. x ÷√16-x^2. c. undefined. d. √16+x^2 ÷ x. e. 4 ÷ √16-x^2 f.none
Name: Lab 3: Differentiation An example to differentiate an expression: To assign the expression 2x-5x+x to the variable fenter: f:-2*x^3-5 *x^2 +x; To enter f(x) -2x3-5x+x as a function enter: f:=x->2*x^3-5*x^2+x To differentiate some function fenter: D (f); To differentiate some diff (f,x) ; expression f with respect to x enter: Now follow the steps in the Example above to differentiate the expression t-1 Keep in mind that you cannot use the variable f for the expression (we already used...
y=4^x+(ln(6))^x+e^π+6^5x+7
# 2,3,4,7, 10,11,15,18) Differentiate the function: #2 f(x) = ln(22 + 1) #3 f@) = ln(cos) #4 f(x) = cos(In x) #7 f(x) = log2(1 – 3x) #10 f(t) = 1+Int #11 F(x) = In( 3+1") #18 y = (ln(1 + e*)] # 23) Find an equation of the tangent line to the curve y = In(x2 – 3) at the point (2,0). # 27, 31) Use the logarithmic differentiation to find the derivative of the function. # 27 y...
Differentiate the function. y = 2x² - 1 8x + 3 y'=0
Find the solution of the given initial value problem: y′′′+y′=sec(t), y(0)=6, y′(0)=7, y′′(0)=−3 Enter ln|a| as ln(|a|). Enclose arguments of functions in parentheses. For example, sin(2x). y(t)=
- 3e - sin(-5x) Find lim - 2x (x,y)+(0,0) -3e - sin(-5x) lim - 2x (x,y)-(0,0) (Type an integer or a simplified fraction.)
2. x+4y= 14 2x - y=1 x=2, y=3 3. 5x + 3y = 1 3x + 4y = -6 x=2, y=-3 | 4, 2y- 6x =7 3x - y=9 No solution/Parallel lines
12. Find the derivative of the following: y = ln(2x + 4x2 - 2x + 4)