(0,F) (L.F) (L+ F, 0) (L+F+ LF, 0) 2. The following is the graph of f'(x).

Q: If f(x) = -csc (G) then f'(x)

A: Given f(x)=-csc(x/2)

Q: For each of the above functions, prove that f(f-1(x)) = f-1(f(x)) = f(x) = +6 f(x) = x3 + 2 f(x)…

A:

Q: x 29. f(x) 1 + e*

A: Differentiating the given function by using quotient rule, we get

Q: a(1+x²) Find the derivative 1-x

A:

Q: Use the graph of the function f(x) to sketch the graph of the derivative f’(x)

A: We have to graph the function f(x) and its derivative.

Q: Where are the functions f1(x) = ∣sin x∣ and f2(x) = sin ∣x∣ differentiable?

A: We graph f1(x) = ∣sin x∣  using a graphing calculator. We see that, at x=nπ, there are cusps.…

Q: f(x) = |x| · : %3D Then f-l(x) = if x > 0, and f-l (x) = if x < 0.

A:

Q: Is the mathematical statement correct. If f(x)=f(-x), then f’(x)=f’(-x). Explain why

A:

Q: Vx 3+x (g(x)) if g(x) = 3x +2 + S, * ** dx c) %3D

A: I applied Leibnitz rule

Q: find the derivative of f(x) = (x²+4)(3x³ - 2x) at the point x = - 3[ use product rule] %3D B.

A: We have to find the derivative

Q: Find the general form of f if f'(x)- 8f(x).

A:

Q: if f''(x) = 0 an inflection point, what can be said aboutthe sign of  f'''(x)?

A: We have to fund the condition for f"' (x) for a inflection point  to happen.

Q: Compute the derivative of f(x)= (ex2 +e-x2 )/(ex2 -e-x2 )

A:

Q: find the derivative of f(x) = (x² +4)(3x³-2x) at the point x =- 3[use product rule]

A:

Q: Find inverse function of (a) y = - x^2 (b) y = 3 - 2x

A:

Q: ermine dy for the following two functions. dx y = 3x¹ + (7 + sin x)²

A:

Q: Determine f '(x) from the first principles if f (x) = -2 -3x

A:

Q: What rule do you use to calculate the derivative of f(x) = exx2 and f(x)=(x2-3x+1)/(x+5) ?

A: Use the product rule and quotient rule of derivative:

Q: evaluate the derivative of the function at the given pointf(x)=-4/(2x2-3x)4 , (1,-4)

A: