(a) Find the derivative of g(x) = 5arctan( for x > 0. Simplify your answer. g'(x) = (b) Find the derivative of h(x) = 5arctan(x) + 5arctan(¹) n(1) for x > 0. Simplify your answer. h'(x) = (c) What does your result in part (b) tell you about h(x) for x > 0 ? Oh(x) is constant. O h(x) is increasing. Oh(x) is decreasing.

Q: Find the derivative of P(x) = -8x¹/9 - 3x -7 Write your answer using negative exponents. P'(x) = =

A: Given,

Q: (b) F₂(x) = F₂'(x) = 9 4(x4 + 1)5 (d) F4(x) = F4'(x) = X 4 (c) F3(x) = (9x² + 1)5 4 F3'(x) = 9 (4x4…

A:

Q: For some function h(x), h'(x)=x^3(x+4)^2 and h''(x)=x^2(x+4)(5x+12). Make sign charts for the first…

A: Use real number line

Q: An unknown function's derivative is h'(x) = 3x-2 - 6. Using your understanding of the derivative…

A:

Q: 9,3 5 y = 10(1 + (2 − (6 + 7x²³)9³)

A:

Q: 2x2 – x +2 Find the derivative f'(x) by hand when f(x) = 12x + 7 f'(x) =

A:

Q: Find the derivative of the function. F(x) = (5x + 2x³14 F'(x) =

A:

Q: 6e + 4 Find the derivative of g(x) 10r5 + 5x3 %3D = (z),6

A:

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: f'(x)=-2x8-x2;(2,8)

Q: Find the derivative of y = (3x4 - 7x + 2)g(x).

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: Find the derivative of -4 f(x) = 6x° /x +

A: Given function :

Q: Find the derivative of the given function. g(x) = sec¹(2πx) a) g'(x) = 87 sec³ (2πx) tan(2x) Ob)…

A: I am attaching image so that you understand each and every step.

Q: The derivative of a function is g'(x) = 19 – 6x² and the graph of g(x) passes through the point P(3,…

A: To find  g(x)