Sample test $4$

Show all your work.

Find $\frac{dy}{dx}$ if $y=9^{x^2}logx\frac{d}{dx}(9^{x^2}logx)$

Find $\frac{dy}{dz}$ if $y=sin(e^{-7z^7})$

Find $\frac{dy}{dx}$ if $y=\frac{e^{2}3}{e^2-2}$

Find $\underset{x{1}^{-}}{lim}(x-1)tan(\frac{}{2}x)$

Find $y^{\text{'}}$ if $tany=e^{-x^3}lo{g}_3{x}^2$

Find $f^{\text{'}}(x)$ if $f(x)=x^{3}ln(cos{x}^4)si{n}^{3}x$

Find $f^{\text{'}}(x)$ if $f(x)=5^{-3x}co{t}^{-1}(8x)$

If $f(x)=2^{x^3}lo{g}_2(x^5-31)$ then $f^{\text{'}}(x)=$

Find $g^{\text{'}}(-1),$ where $g$ is inverse function of $f(x)=x^5{x}^{2}12.$

Find $\frac{dy}{dx}$ if $y=(tanx{)}^{sinx}$

For the questions $11$ and $12$: Given $F(x)=4x^3-15x^2-18x10$

$11.F(x)$ has a relative maximum at $x=$

$($a$)3($b$)\frac{1}{2}$

$($c$)1$

$($d$)-\frac{1}{2}$

$($e$)$ Cannot be determined

$12.F(x)$ has a

point of inflection at:

$($a$)\frac{3}{4}$

$($b$)-\frac{1}{4}$

$($c$)3$

$($d$)\frac{5}{4}$

$($e$)-\frac{1}{2}$

$13.y=3x^4-4x^{3}1$ has

$($a$)$ a relative maximum at $x=0$; no relative minimum

$($b$)$ no relative maximum; a relative minimum at $x=6$

$($c$)$ a relative maximum at $x=0$; a relative minimum at $x=1$

di$)$ ho relative maximum; a relative minimum at $x=1$

$($e$)$ a relative minimum at $x=0$; a relative maximum at $x=1$