# Math Help - derivatives

1. ## derivatives

Hi,

Q1.
a) At what rate is the radius of a spherical balloon changing at the time that the radius is 10cm, if air is being pumped in at a rate of 40 cm^3 s^-1 ?

b) Find an expression for dy/dx given that 3xy + e^y = 3.

If there is anything unclear, let me know, thanks in advanced.

2. Q1.
a) At what rate is the radius of a spherical balloon changing at the time that the radius is 10cm, if air is being pumped in at a rate of 40 cm^3 s^-1 ?
$\frac{d}{dt}\left(V = \frac{4}{3}\pi r^3\right)$

$\frac{dV}{dt} = 4\pi r^2 \cdot \frac{dr}{dt}$

you were given $\frac{dV}{dt}$ and $r$ ... solve for $\frac{dr}{dt}$

b) Find an expression for dy/dx given that 3xy + e^y = 3.
$\frac{d}{dx}(3xy + e^y = 3)$

$3x \cdot \frac{dy}{dx} + 3y + e^y \cdot \frac{dy}{dx} = 0$

solve for $\frac{dy}{dx}$