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    Hey,

    I was wondering if someone could help me with these questions?

    4. Find the gradient of the tangent to the curve y=tan^{-1}(3x) where x= 1/sqrt 3

    I know that you need to use product rule, but I think my value of u is wrong, although I'm not sure what's correct.

    I said u=ln3x; v=tan^{-1}3x


    7. Given 1/x + 1/y = 1/pi, find dy/dx and d^2y/dx^2


    8. Given y=2^x/(x+2), find the rate of change of y with respect to x, when x=2

    I get the answer ln2 - 1/4 but the actual answer is ln2+1/4


    10. A curve is defined parametrically by x=2t - 3 -1/t,      y=t - 1- 2/t

    a) i) Find the equations of the tangents to the curve at the points where it crosses the x-axis

    I worked out that dy/dx = 3/2, but I don't think this is correct!

    Thanks
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    For 4, rewrite as 3x=tan(y) to make things easier.

    For 7, rearrange the equation to get y on its own on one side of the equation, then the quotient rule will be handy.

    For 8, I agree with you.

    For 10, there are 2 places where the graph crosses the x axis, how have you found these?
 
 
 
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