Let f(x) = x ln(1+ x*). For all æ € [-1, 1], it is known that In(1 + x) = (-1)" -xn+1 n +1 n=0 2. Evaluate f(1804) (0), i.e., the 1804th derivative of f at x = 0.

Q: Option 2: Problem Solving You wish to invest P10,000 for a period of 5 years. Which of the following…

A: The principal amount we have is ₱10000 and the time period is 5 years.  Therefore,  P=₱10000 t=5

Q: (g) Suppose the first derivative of f(x) is f'(z) = z - 62 + 11z – 6. Where is f(z) increasing? Use…

A:

Q: Let 60, 61. What is the derivative of the function y = b²? In(b) -In(x) 1 1 In(b) ○ b* In(b) eIn(b)…

A: Option (c) is the right answer. Explanation:

Q: Suppose that f (x) is a function with f (0) 1 and f' (0) = 3.1 If g(x) = (f (x))³ , then what is the…

A: We find value of g'(0)

Q: Use the table below to find h'(-1) for h (x) = f (g (x)). I()9() lO() 1/2 0. -2 -3 1. -1 -1 -2 -2 -2…

A: Given that hx =fgxTo find : h'-1Solution hx =fgxh'x =f'gx×g'xx=-1h'-1 =f'g-1×g'-1h'-1 =f'-2×2h'-1…

Q: 11. f(x) =log, 1+x

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: If g(x) = In(12x7 – x), then the derivative of g'(x) is O 12x7 – x | O 84x6 1 84x6 1 12x7 O 726 12x7…

A:

Q: (d) Use the following table to evaluate each derivative. I 0 1 2 f(x) 1 3 -2 g(x) f'(x) 1 2 4 -3 0.5…

A: Since you have posted multiple questions i can do first question as per our company guidelines,…

Q: Let f(x) = (x² + 3x)e*. Determine the value of the third derivative of f(x) for x = 0.

A:

Q: Suppose g(x)= 3 2(1–5x)3 k (1–5x)4' with a derivative g'(x) = - " for some real number k. What is…

A:

Q: Suppose g and h are functions such that g (x) = ln (1 + h (sqrtx)). Find g'(4), given that h'(2) = 1…

A:

Q: Find the coordinate vector [x]B of the vector x relative to the given basis B. 23) b1 =| b2 and B =…

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Q: h(x) = In (a- 7) (r +3)

A:

Q: Recall for a given function g, when  g'(x) > 0  for each value of x in an interval  (a, b),  then…

A: Here, we are going to use ''First derivative test''

Q: 5. If f(x) = x², g(x) = and h(x) = √x² + 2x, determine the derivative of each composite function. a.…

A: Given: f(x)=x2,g(x)=1x′ and h(x)=x2+2x First find the composite functions and then differentiate

Q: 1)-Define the following and give an example: Derivative function - Logarithm function

A: We need to define derivative and log function. As per Bartleby guidelines we can solve one question…

Q: 4. Find the derivative of r°(x+ 1)² y = Vr – 3x2 |

A: First i i have written the quotient rule of derivative , just use them for given function and get…