Question

How do you differentiate `f(x)=(x^1.7+8)/(x^1.4+6)` using the quotient rule?

Answer 1

`f^'(x)=(0.3x^2.1 +10.2x^0.7 -11.2x^0.4)/[(x^1.4 +6)^2]`

Explanation:

Given -

`f(x)=(x^1.7 +8)/(x^1.4 +6)`

`f^'(x)={[(x^1.4 +6)(1.7x^0.7)]-[(x^1.7 +8)(1.4x^0.4)]}/[(x^1.4 +6)^2]`

`f^'(x)={[1.7x^2.1 +10.2x^0.7]-[1.4x^2.1 +11.2x^0.4]}/[(x^1.4 +6)^2]`
`f^'(x)=(1.7x^2.1 +10.2x^0.7-1.4x^2.1 -11.2x^0.4)/[(x^1.4 +6)^2]`
`f^'(x)=(0.3x^2.1 +10.2x^0.7 -11.2x^0.4)/[(x^1.4 +6)^2]`