2 Differentiate with respect to \( x \) : (a) \( y=\sin ^{-1}(3 x+2) \) (d) \( y=\cosh ^{-1}(1-3 x) \) (b) \( y=\frac{\cos ^{-1} x}{x} \) (e) \( y=\sinh ^{-1}(\cos x) \) (c) \( y=x^{2} \tan ^{-1}\left(\frac{x}{2}\right) \) (f) \( y=\tanh ^{-1} 5 x \)
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The questions are all very straightforward and should not cause you any anxiety. Differentiate with respect to $x$ : (a) $y=\sin ^{-1}(3 x+2)$ (d) $y=\cosh ^{-1}(1-3 x)$ (b) $y=\frac{\cos ^{-1} x}{x}$ (e) $y=\sinh ^{-1}(\cos x)$ (c) $y=x^{2} \tan ^{-1}\left(\frac{x}{2}\right)$ (f) $y=\tanh ^{-1} 5 x$
Differentiation applications
Test exercise F.8
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