"Find the first derivative of the following functions..." solved and explained

aidmoon2x

Answered question

2021-11-26

Find the first derivative of the following functions and inverse trigonometric functions. Use the formulas
19.

θ = \arccos \sqrt{1 - x}

Answer & Explanation

Tionant

Beginner2021-11-27Added 17 answers

Given $θ = \arccos \sqrt{1 - x}$
Apply differentiation nale
$[{\arccos (u (x))}^{'} = \frac{- 1}{\sqrt{1 - {(u (x))}^{2}}} u^{'} (x)$
heve $u (x) = \sqrt{1 - x}$
$u^{'} (x) = \frac{d}{d x} {(1 - x)}^{\frac{1}{2}}$
Agply, power ale ${({f (x)}^{n})}^{'} = n {f (x)}^{n - 1} . f^{'} (x)$
$u^{'} (x \frac{1}{2} {(1 - x)}^{\frac{1}{2} - 1} \frac{d}{d x} (1 - x)$
Applu ${(f \pm 9)}^{'} = f^{'} \pm 9$
${(a^{n})}^{'} = n x^{n - 1}, \frac{d}{d x} (c o n s t a n t) = 0$
$u^{'} (x) = \frac{1}{2 \sqrt{1 - x}} (0 - 1) = \frac{- 1}{2 \sqrt{1 - x}}$
$(\arccos {\sqrt{1 - x}}^{'} = \frac{- 1}{\sqrt{1 - (1 - x)}} [\begin{matrix} \frac{- 1}{2 \sqrt{1 - x}} \end{matrix}]$
$\frac{d θ}{d x} = \frac{1}{2 \sqrt{1 - x} \sqrt{x}}$

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