11 multiple choice 1 point if f(x)=arccos(x²), then f(x)=(a) 1/√(1 - x⁴) (b) -2x/√(1 - x⁴) (c) 2x/√(1 - x⁴)…

Answer:

B. $\frac{-2x}{\sqrt{1 - x^{4}}}$

Explanation:

Step1: Recall derivative of arccos(u)

The derivative of $y = \arccos(u)$ with respect to $x$ is $y'=-\frac{u'}{\sqrt{1 - u^{2}}}$ by the chain - rule. Here $u = x^{2}$.

Step2: Find the derivative of u

If $u=x^{2}$, then $u'=\frac{d}{dx}(x^{2}) = 2x$ using the power - rule $\frac{d}{dx}(x^{n})=nx^{n - 1}$ with $n = 2$.

Step3: Substitute u and u' into the formula

Substitute $u = x^{2}$ and $u'=2x$ into the formula for the derivative of $\arccos(u)$. We get $f'(x)=-\frac{2x}{\sqrt{1-(x^{2})^{2}}}=-\frac{2x}{\sqrt{1 - x^{4}}}$.