# Thread: differentiate y= arcosh (4+3x)

1. ## differentiate y= arcosh (4+3x)

differentiate y= arcosh (4+3x)

could anyone help me please . what differentiation rule do i use with this equaiton and what answer should i get please thankyou !!!!

2. Hello there,

I assume you mean: $\displaystyle \frac{d}{dx} ( cos^{-1}(4 + 3x))$.

Recall that $\displaystyle \frac{d}{dx} cos^{-1}(x) = -\frac{1}{\sqrt{1 - x^2}}$.

Be sure to use Chain Rule when differentiating.

Good luck! This should be enough information.

3. No, this is the inverse of hyperbolic cosine.

Hyperbolic cosine is

$\displaystyle \cosh x={e^x+e^{-x}\over 2}$ and $\displaystyle \sinh x={e^x-e^{-x}\over 2}$

See http://en.wikipedia.org/wiki/Hyperbolic_cosine.

The inverse of cosh can be obtained via algebra, letting $\displaystyle w=e^x$.

But you can see the derivative of the inverse of cosh at that page, then via the chain rule you can solve this problem.

4. Originally Posted by lukyleo26
differentiate y= arcosh (4+3x)

could anyone help me please . what differentiation rule do i use with this equaiton and what answer should i get please thankyou !!!!