[8] Use the definition f(a +h) – f(a) f'(a) = lim h-0 h To find the derivative of the given function at the given value of a. f(x) = 1/x,a = 2

Q: f(x+h)-f(a) a.) Find the derivative function, f'(x) = lim h-0 b.) Determine the slope of the curve,…

A:

Q: f(x+h) – f(x), Use the definition of the derivative (that is, f'(x) = lim h0 3 = 3r2. dr to show…

A:

Q: Determine where the function f(x) is decreasing given the first derivative is: ƒ¹(x) = x²(x + 1)

A:

Q: Given the function, find the derivative f (x) = -()" 3z 4 3z- 3 12() 3z-4 O None of the Above

A:

Q: Determine the derivative of f(x) =2x/x2+1 using the quotient rule and find the equation of the…

A:

Q: Exercise 5: For the following graphs, sketch a graph of the derivative (i.e., you are given f;…

A: Consider the given curve of f(x).

Q: a) Prove that (arctan r 1+2 b) Using part(a), find the derivative of f (x)= arctan (208 )

A: Properties of derivative  f(g(x))=f'(g(x)) g'(x)ddxcosx=-sinxddxax=axloga

Q: 9. f(x) = -4x5 + cot-1 x 10. f(x) = csc x sec-x %3D

A: 9. Given: fx=-4x5+cot-1 x  ……1

Q: Find the general form of f if f'(x)= -7f(x).

A:

Q: Explain why the derivative of a 2x – 3 is two, i.e. if f(x) = 2x – 3, then f’(x) = 2. Use proper…

A:

Q: Consider the function 2x + 1 g(x) = x +1 a) Evaluate the derivative of the function. b) Sketch the…

A:

Q: Determine f ″ ( x ) for f(x) = sec x

A: Given function: fx=secx

Q: Use the definition f'(x) = f(x) = 6 6 - 6x O-12x² -12x 6 - 12x lim f(x + h)-f(x) h h-0 6x² to find…

A: To find the derivative of the given function

Q: The functionf(x) is Find the first derivative in fa Set up a number line with t increasing,…

A: The given function is fx=3x5-5x4. Find the first derivative of the function by the power rule of…