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Differentiate $ln(\sec x+ \tan x)$ and $ (\sin x)^3\cos 3x+ (\cos x)^3\sin 3x$ with respect to $x$, simplifying where possible.

Find the first and second derivatives (with respect to x) of the function $x= \sin(t^2+t+2)$ $y= 5^t$

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Using $$\sin3x=3\sin x-4\sin^3x,\cos3x=4\cos^3x-3\cos x$$

$$\sin^3x\cos3x+\cos^3x\sin3x$$ $$=\frac{(3\sin x-\sin3x)\cos3x+(\cos3x+3\cos x)\sin3x}4=\frac34(\sin x\cos3x+\cos x\sin3x)=\frac34\sin(x+3x)$$

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what about the ln differentiation and the derivative? –  Alexanderakk Nov 18 '13 at 15:58
@DK.H, use en.wikipedia.org/wiki/Chain_rule for the $\ln$ and the last $\sin$ function –  lab bhattacharjee Nov 18 '13 at 16:00

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