1. Write in the form au^n is: a (1)/((2x-1)^2) sqrt (x^2-3x) C (2)/(sqrt (2-x^2)) d sqrt [3](x^3-x^2) (4)/((3-x)^3) f (10)/(x^2)-3 2 Find the gradient function (dy)/(dx) for: a y=(4x-5)^2 b y=(1)/(5-2x) y=sqrt (3x-x^2) d y=(1-3x)^4 e y=6(5-x)^3 f y=sqrt [3](2x^3-x^2) g y=(6)/((5x-4)^2) h y=(4)/(3x-x^2) y=2(x^2-(2)/(x))^3 3 Find the gradient of the tangent to: a y=sqrt (1-x^2) at x=(1)/(2) b y=(3x+2)^6 at x=-1 C y=(1)/((2x-1)^4) at x=1 d y=6times sqrt [3](1-2x) at x=0 e y=(4)/(x+2sqrt (x)) at x=4 f y=(x+(1)/(x))^3 at x=1 7

1. The correct answer is option a: .Explanation: The expression can be written in the form , where is a constant, is a variable, and is a positive integer. In this case, , , and .2. The gradient function for each of the given functions is as follows:a) b) c) d) e) f) g) h) i) 3. The gradient of the tangent to each of the given functions at the specified points is as follows:a) at b) at c) at d) at e) at $\frac {dy}{dx} = -\frac {4(1+\frac {1}{\sqrt {x}})}{(x+2\sqrt {x})^{2}} \cdot