Gives an example of calculating the first and second derivatives of a function where implicit differentiation is required

Shows how to solve an equation of the form ax^4+bx^2+c=0 by first making the substitution u = x^2 so that the associated quadratic equation in terms of u can be solved first, using the quadratic formula. It is then easy to find the values of x, by first substituting back x^2 for u.

Introduces how to use implicit differentiation to find dy/dx for an example where the use of the product rule is also required

Introduces how to use implicit differentiation to find dy/dx for an example where the use of the quotient rule is also required

Introduces how to use implicit differentiation to find dy/dx for an example

We investigate the rule for differentiating an inverse function then make some observations about reciprocals of 1st and 2nd derivatives.

We use the complex exponential to integrate e^(ax) times cos(bx) or sin(bx) as real and imaginary parts of the same integral. Integration by parts is thereby avoided.

In this recording we look at a second example of how to write a composite hyperbolic function as an algebraic function of x.

Example of using differentiation by first principles to evaluate the derivative of the function y = square root of x

Example of using differentiation by first principles to evaluate the derivative of a quadratic function.