Which statement is false? a. The derivative ƒ'(a) is the instantaneous rate of change of y = f(x) with respect to x when x = a. b. The average rate of change of y = f(x) is the same as the slope of the secant line through (x₁, y₁) and (x2, y2). C. The derivative f'(a) is the average rate of change of y = f(x) with respect to x when x = a. d. The instantaneous rate of change of y = f(x) with respect to x when x = a is the same as the slope of the tangent to y = f(x) at x = a.

Q: What is the derivative of the function f(x)=1/x+1 at x=1?

A: To find out the derivative of the function at x=1

Q: Find the derivative. h'(w) = = h(w) = (w4 - 5w)4 4(w² - 5w) ³. (4w ³ - 5) x

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Q: Find the derivative of the function h(w) = -7w¯4 +6/w. %3D h'(w) :

A: The function is  h(w) =-7w-4+6w. We know that derivative of wn, i.e., dwndw = nwn-1.

Q: Find the derivative of the function y= arctan x +x/1+x2

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Q: compute the derivative

A:

Q: Find the derivative () of: dx y = 4x Jx + Vx

A: Using chain rule of derivative it can be done. please follow the solution which is mentioned in step…

Q: f'(x) represents the slope of the secant line at any point on the graph of the function.

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Q: dx Evaluate xx2 - 1

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Q: Find the derivative of the function f(z) = 3z² +7z at I = a.

A: Given,            f(x) =3x2 + 7x  and x=a

Q: Find the value of the derivative of the function f (x) = 16 - |x| at the extremum point ( 0, 16)

A: We have to find the value of derivative of the function f(x) = 16 - |x| at the extremum point…