20. Differentiate. (2 pts each)(a) y= In(x In x)(b) y = e cos nxe/x(c) y=x2(d) y = ln sec x(e) y= Varctan x(f) y = x cos-'x

Let's differentiate one by one: a) Differentiate using the chain rule, which states that (d)/(dx)[f(g(x))] is f'(g(x))g'(x) where f(x)=\ln (x) ...

Resuelto 20. Differentiate. (2 pts each)(a) y= In(x In

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Pregunta: 20. Differentiate. (2 pts each)(a) y= In(x In x)(b) y = e cos nxe/x(c) y=x2(d) y = ln sec x(e) y= Varctan x(f) y = x cos-'x
$20 .$ Differentiate. $(2$ pts each $) ($ a $)$ y $=$ In $($ x In x $) ($ b $)$ y $=$ e cos nxe $/$ x $($ c $)$ y $=$ x $2 ($ d $)$ y $=$ ln sec x $($ e $)$ y $=$ Varctan x $($ f $)$ y $=$ x cos $-'$ x
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Solución
Paso 1
Let's differentiate one by one:
a)
$\begin{aligned} \frac{d y}{d x} & = \frac{d}{d x} \ln (x \ln x) \end{aligned}$

Explanation:
Differentiate using the chain rule, which states that $\frac{d}{d x} [f (g (x))]$ is $f^{'} (g (x)) g^{'} (x)$ where $f (x) = \ln (x)$ ...
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