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Differientiate the function and tangent line

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Please answer the attached problems and circle the answers. thanks

1. Differientiate g(x) = (7x - 5)/(5x + 1) + x^3

2. Find dy/dx, y = x^0.75

3. Differientiate the function y = sqrt(x^2 + 6)

4. Find an equation for the line that is tangent to the curve y = 4x^3 - 4x at the point (1, 0)

5. For the function, find the points on the graph at which the tangent line is horizontal. y = 2x - 1
a) The tangent line is horizontal to the graph at
b) there is no solution

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Solution Summary

It provides several examples of finding the derivatives of the functions. It also shows how to find out the tangent line to the curve.

Solution Preview

1) By addition rule and quotient rule,

2)

3) By chain rule:

4) The slope of the tangent line is the ...

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