Master Calculus 1 Practice Problems with Expert Help

Find the derivative of the function.
1) $f(x)=\arcsin (x-1)$
2) $f(x)=\arccos \sqrt{x}$
3) $f(x)=\arctan e^x$
4) $f(x)=\sin (\arccos x)$

Suppose $y=\sqrt{2x}+1$, where x and y are functions of r.
(a) If $\frac{dx}{dt}=3$, find $\frac{dy}{dt}$ when $x=4$.
(b) If $\frac{dy}{dt}=5$, find $\frac{dx}{dt}$ when $x=12$.

find $\frac{dy}{dx}$
${\displaystyle f\left(x\right)=x^2\sin \left(x\right)}$

Which of the following is NOT a result of the Central Limit​ Theorem? Choose the correct answer below. 
a) As the sample size increases, the distribution of the sample means x-bar will approach a normal distribution.
b) The distribution of the sample data will approach a normal distribution as the sample size increases. 
c) The variance of all sample means is the population variance divided by the square root of the sample size.
d) The mean of all sample means is the population mean $\mu$

Given ${\displaystyle f(x,y)=2x^2-x{y}^3+4y^6}$, find
${\displaystyle f_{xx}(x,y)=}$
${\displaystyle f_{xy}(x,y)=}$

Discover all the functions' second-order partial derivatives. ${\displaystyle f(x,y)=\sin xy}$

Find the critical points of: ${\displaystyle f(x,y)=e^{x-y}}$
-None
$-(-1,1)\mathrm{\&}(1,-1)$
${\displaystyle -(t,t):t\in R}$
${\displaystyle (t,-t):t\in R}$