Question

How do you differentiate `f(x)=sqrtcos(e^(4x))` using the chain rule.?

Answer 1

`f'(x) = frac{-2sin(e^(4x)) e^(4x)}{sqrt(cos(e^(4x)))}`

Explanation:

Let

• `p = 4x`
• `q = e^p`
• `r = cos(q)`
• `s = sqrtr`

Therefore, to differentiate `f(x)`, we need to find `f'(x)`, which is the same as `frac{"d"s}{"d"x}`.

Applying the chain rule,

`frac{"d"s}{"d"x} = frac{"d"s}{"d"r} frac{"d"r}{"d"q} frac{"d"q}{"d"p} frac{"d"p}{"d"x}`

`= 1/(2sqrtr) * (-sin(q)) * e^p * (4)`

`= frac{-2sin(e^(4x)) e^(4x)}{sqrt(cos(e^(4x)))}`