Get the solution to "Find the derivatives of the following functions. f(x)=cos⁡h−14x"

allhvasstH

Answered question

2021-04-11

Find the derivatives of the following functions.

f (x) = {\cos h}^{- 1} 4 x

Daphne Broadhurst

Skilled2021-04-13Added 109 answers

Step 1:Formula used

\frac{d}{d x} ({\cos h}^{- 1} x) = \frac{1}{\sqrt{x^{2} - 1}}

Step 2:Calculation
Consider the following function

f (x) = {\cos h}^{- 1} 4 x

Differentiating with respect to x and applying chain rule, we get,

f^{'} (x) = \frac{d}{d x} ({\cos h}^{- 1} (4 x))

\Rightarrow f^{'} (x) = \frac{1}{\sqrt{{(4 x)}^{2} - 1}} \cdot \frac{d}{d x} (4 x)

\Rightarrow f^{'} (x) = \frac{1}{\sqrt{{(4 x)}^{2} - 1}} \cdot 4

\Rightarrow f^{'} (x) = \frac{4}{\sqrt{(4 x + 1) (4 x - 1)}} [∵ a^{2} - b^{2} = (a + b) (a - b)]

Hence,

f^{'} (x) = \frac{4}{\sqrt{(4 x + 1) (4 x - 1)}}

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