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The derivative of $\cos^{-1}x$ is
A$\dfrac{1}{\sqrt{1-x^2}}$
B$-\dfrac{1}{\sqrt{1-x^2}}$
C$\dfrac{1}{1+x^2}$
D$-\dfrac{1}{1+x^2}$
Answer & Solution
Correct answer: B. $-\dfrac{1}{\sqrt{1-x^2}}$
The derivative of $\cos^{-1}x$ is the negative of the derivative of $\sin^{-1}x$: $\dfrac{d}{dx}(\cos^{-1}x)=-\dfrac{1}{\sqrt{1-x^2}}$.
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