Find the function f given that the slope of the tangent line at any point (x, f(x)) is f'(x) and that the graph of f passes through the given point. 2x f'(x) = 1 - (0, 6) x² + 1 f(x) = Need Help? Read It

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A: A detailed solution is given below

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A: use implicit differentiation, I try to provide typed solution, if it is helpful like it.

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A: Applying natural logarithm on both sides, we get

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Q: 7) Find the average rate of change of the function A(x) = sin ( 2x - -) from x = to x =

A: A(x) = sin(2x - π/6) A(x2) = A(5π/6)          = sin(2*5π/6  - π/6)          = sin (9π/6)          =…

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A: Given: y=sinsinsinx

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Q: Compute the derivative of the function y = 5 sin-'(x) at the point x (Use symbolic notation and…

A: We know, ddxsin-1(x)=11-x2

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A: Explained below

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Q: Find the equation of the tangent line to the graph of f(x) = In(-x) at x = x0 = -e'. =-e?. Equation:

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A: Let's draw the graph of f''(x).