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here the student needs to use both implicit differentiation and the product rule.

I would differentiate term by term for this problem.

for 2ye^-3x you have to use the proudct rule. uv differ...

A quadratic equation is one that takes the form.. ax² + bx +c = 0

Factorising an equation like this involves putting the equation into two brackets.

The method varies slightly dep...

9/3x² - 3y² + x/xy - x² = 9/3(x²-y²) + x/x(y-x) = 3/(x-y)(x+y) + 1/y-x = 3/(x-y)(x+y) - 1/x-y = 3-1(x+y)/(x-y)(x+y) = 3-x-y/(x-y)(x+y)

We will split this up and differentiate each part separately.

We can differentiate 4x² using our normal rules for differentiating; we multiply the coefficient by the pow...

y=(4x+1)^3*sin(2x) - this is a product of two functions of x. It can be rewritten as y = u(x)*v(x)   ; where u(x) = (4x+1)^3 and v(x) = sin(2x)

Using the product rule: dy/dx = u'(x)*v(x) + v'(x)*u(...