Suppose f E C" (IR). Show directly that a fixed point xo is exponentially stable if f' (xo) < 0 and unstable if f' (xo) > 0.

Q: If f(x) = x + VT, find f' (1)

A:

Q: Let f(x)=9x^2/4−3x then  f'x= f''x=

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: If f(x) = log(a)x, show that f(x^α) = αf(x).

A: Given that:

Q: Suppose that f(x) = log4 (4x + 1). Find f' (2). f' (2) =

A:

Q: Find f''(x) if f(x) = e^3x^2+1.

A: calculate the second derivative for the given function

Q: If f(x) = 6x'n (=), find f'(2).

A: We first take ln on both sides and expand the right side

Q: Suppose F(x) = f(x² + 1). Find F'(1) if f'(2) = 9.

A:

Q: Suppose that f'(0) = 2. Find the derivative of the function (e2z – 2x)f(3x) at x = 0.

A: Given that f'(0)=2.Our Aim is to find the derivative of the function (e2x-2x)f(3x)-(i) at x=0.

Q: If f(x) is a constant function, then f'(x) is zero. True False

A:

Q: Suppose that f(4) = 4, g(4) = 3, f'(4) = -2, and g'(4) = 5. Find h'(- %3D h (x) g(x) f(x)+g(x) '…

A:

Q: Let f(x) = e³x²(9x − 2). Compute f'(x). f'(x) =

A:

Q: Suppose that f(x) = 4e"- ex. Find f'(3). %3D

A: we will first find out the derivative of f(x) and then we put x=3 in the derivative to get f'(3).

Q: Let f(x) - 6e* +2 + e'. f'(0) =

A: The given function is f(x)=-6ex+2+e1

Q: true or false prove your answer If (an) is Cauchy and p is a number such that for infinitely many…

A: Given that              an is a Cauchy sequence and p is a number such that for infinitely many…

Q: Let f (x) = x² 2 - 8 Find and simplify f'(x) and f" (x). + B where f'(x) = A = B = C = %3D Dx2 + E…

A:

Q: Let f(x) = log, (8x? 3x + 10). Find f' (x).

A: Differentiation wrt x

Q: What is f’(2) for the function attached below?

A: We have to calculate the derivative of the given function at x=2 f'(2)…

Q: Find y=f(x) if f''(x)=4x^2, f'(0)=3, and f(0)=2.

A:

Q: If f(æ) = 3 + 3 find f'(x). Find f'(1). Find f''(x). Find f''(1).

A:

Q: If f(x) = (3x + 8), find f'(x). %3D Find f'(1).

A: Note some formule:

Q: find f'(t) for f(x)=x/8x-8

A: We will need the quotient formula to find f'(x) Assume u and v, then find u' and v'

Q: Suppose F(x) = f( x3 + 1 )   Find F'(1) if f'(2) = 5

A:

Q: Suppose that f'(4) = g(4) = g'(4) = 1. Do we have enough information to compute F'(4), where F(x) =…

A: f'(4) = g(4) = g'(4) = 1