Hence determine the tangent to the curve at the point (-2,1)

A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 0.5ms-1. How rapidly is the area enclosed by the ripple increasing when the radius has become 5m?

Hint: This is a related rates question. A suggested start is to assign letters to all quantities that vary and then identify the known rates and the rate that is to be found.

Graph on the same axis:

1. y = 1/x

2. y = 1/x-3

3. y = 2 + (1/x-3)

Clearly label key points (eg. turning points, end points, discontinuities, etc if these exist).

Question 3: a) Find the derivative of the following functions dy/dx, by the method of implicit differentiation: i) (x^2)(y^2) - xy = 8; ii) sqrt(x + y) = x; iii ...

... The expert uses the implicit differentiation and finds open intervals. 3 questions on Calculus homework. ...Find the derivative of the function. ...

... It helps find the indicated higher order derivative of functions. THE DIFFERENTIATION OF ALGEBRAIC FUNCTIONS. Use implicit differentiation to find the dy/dx: ...

...Implicit differentiation Implicit differentiation is a technique based on the Chain Rule that allows us to ... For example, we can find the derivative of the ...

... Then to find , we follow the implicit differentiation techniques. Logarithmic differentiation Logarithms are also used for finding derivatives of complicated ...

... This process of differentiation is called 'Implicit differentiation'. ... independent variable, we carry out this kind of differentiation. ...Find the derivative; ...

1. Find the rate of change dy/dx where x = x0 (Compute the derivative of the function from the definition only ... 3. Find dy/dx by implicit differentiation. ...

... Hence, the tangent line equation can be written as: It shows how to find the derivative and equation of tangent line by implicit differentiation. ...

... 2. Find dy/dt =5 2 +3. 3. Use implicit differentiation to find dy/dx +3 + =8. 4. Find the derivative of y with respect to x, t, or 0 as appropriate. 1 = − 3. ...