Calculus Problem Solver & Examples

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

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

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

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) ${\displaystyle \frac{2x}{1+{(x^2+1)}^2}}$

$y(x^2-1)dy+x(y^2+1)dx=0$

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?

Find the point(s) of intersection of the following two parametric curves, by first eliminating the parameter, then solving the system of equations.
${\displaystyle x=t+5,y=t^2\text{and}x=\frac{1}{16}t,y=t}$
a. (25, 400)
b. (1, 16)
c. (400, 16)
d. A and B
e. A and C

Find ${\displaystyle \frac{d^{3}y}{{dx}^3}}$ for the following parametric equation:
$x=t^2-3$
$y=t^8$
$t=2$