Master Calculus 1 Practice Problems with Expert Help

Find the derivatives of ${\displaystyle f\left(x\right)=\frac{3}{2}{x}^4+2x^3-5x^2+9}$

Find the derivatives of ${\displaystyle h\left(x\right)=(-7(x^2-8)2)2x}$

$\int x^3+3\frac{x^2}{x^2}+1$

${\int }_0^{-2}\ln \left|x\right|dx$

Determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data. for those that are exponential, find an exponential function that models the data. 

$\begin{array}{}x& \text{g(x)}\\ \text{−1−1}& \text{3}\\ \text{0}& \text{6}\\ \text{1}& \text{12}\\ \text{2}& \text{18}\\ \text{3}& \text{30}\end{array}$

${\int }_9^4(\sqrt{x}+\frac{1}{\sqrt{x}}{)}^{2}dx$

Need help with the following question Compute the directional derivative of
${\displaystyle f(x,y)=e^{2}x-5y}$

Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as "divergent".
${\int }_3^{\mathrm{\infty }}\left(\frac{8}{{(x+4)}^3}/2\right)$

$\int 2x^2+2x-7x-6$

Consider a first order differential equation
$\frac{2t}{1+t^2}y+\frac{2}{1+t^2}$

Define ${\displaystyle g(x,y)=x^2+y^2-4xy+3y+2}$

Find the derivative ${\displaystyle \frac{d}{dx}\left[\arctan (x^2+1)\right]}$
a) ${\displaystyle {\left(arc\sec (x^2+1)\right)}^2}$
b) ${\displaystyle \frac{1}{2+x^2}}$
c) ${\displaystyle \frac{1}{1+{(x^2+1)}^2}}$
d) ${\displaystyle \frac{2x}{1+{(x^2+1)}^2}}$

Find the point on the line $y=4x+3$ that is closest to the origin.
(x,y)=( )

Find ${\displaystyle \frac{dy}{dx}}$ and ${\displaystyle \frac{d^{2}y}{{dx}^2}}$.
${\displaystyle x=e^t,y=t{e}^{-t}}$
For which values of t is the curve concave upward?