Differentiation of equation

Question

Can you help me differentiate y=(4x^2+4)/5 and explain why you should not use the quotient rule for this?

Answer 1

You could use quotient rule and would get the same answer that Michael showed you, but it is an overkill and unnecessary when the denominator is just a constant. I think it would be a good exercise to try and use it and see what happens.

 

using the quotient rule you would have (8x*5 - 0*(4x²+4)) / 5²  = 40x/25 = 8x/5

 

In general f(x)/c where c is a constant, if you apply quotient we have (f'(x)*c - 0*f(x))/c²

Note that the second part in the numerator becomes zero leaving f'(x)*c/c²

= f'(x)/c 

Answer 2

Rewrite the function as a product.

 

y = (1/5)(4x² + 4)

 

y = (4/5)x² + (4/5)

 

 

Now use the power-rule to differentiate.

 

y' = (8/5)x