Please answer every part! Find the derivatives of the following functions using the Chain Rule: (i)
u(x)=cot(4x^(7)-3x^(3)+4)+ln(sin(x))
(ii)
v(x)=e^(cos(x^(2)))-\root(6)((1)/(x^(2)))
Find the following limits using L'Hopital's Rule: (a)
\lim_(x->1^(+))(5x^(4)-3x-2)/(cos^(-1)(x))
(b)
\lim_(x->(\pi )/(2^(-)))sin(2x)sec(-7x

Question

Please answer every part! Find the derivatives of the following functions using the Chain Rule: (i)

u(x)=cot(4x^(7)-3x^(3)+4)+ln(sin(x))

(ii)

v(x)=e^(cos(x^(2)))-\root(6)((1)/(x^(2)))

Find the following limits using L'Hopital's Rule: (a)

\lim_(x->1^(+))(5x^(4)-3x-2)/(cos^(-1)(x))

(b)

\lim_(x->(\pi )/(2^(-)))sin(2x)sec(-7x

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