Knowledge $/$ Understanding $[15$ marks$]$

Identify the choice that best completes the statement or answers the question.

If $f(x)=si{n}^2(x),$ find $f^{\text{'}}(\frac{}{4}).$

a$.0$

c$.\frac{1}{2}$

b$.1$

d$.\frac{2}{\sqrt[\phantom{2}]{2}}$

If $f(x)=\frac{sinx}{cosx},$ find $f^{\text{'}}(\frac{}{4}).$

a$.1$

c$.\frac{1}{\sqrt[\phantom{2}]{2}}$

b$.-2$

d$.2$

Find the slope of the tangent to the curve $y=2si{n}^{3}x$ at $x=\frac{}{4}.$

a$.\frac{1}{\sqrt[\phantom{2}]{2}}$

c$.-1$

b$.\frac{3}{\sqrt[\phantom{2}]{2}}$

d$.\frac{-3}{\sqrt[\phantom{2}]{2}}$

Find the slope of the tangent to the curve $y=3xcosx$ at $x=.$

$-3$

c$.3$

a$.$

b$.0$

d$.6$

Find the slope of the tangent to the curve $y=4si{n}^{3}2x$ at $x=\frac{}{6}.$

a$.-3$

c$.\frac{3\sqrt[\phantom{2}]{3}}{2}$

b$.6$

d$.9$