## Andresfon12 2 years ago find the partial derivatives

1. Andresfon12

$a) \frac{ z }{ y }| (1, 1/2) if z= e^{x+2y} \sin y$ b) fx (pi/3, 1) if f(x, y) = x ln (y cos x)

2. ZeHanz

a) I don't understand, maybe something went wrong with typing in the formula? b) You need fx, so consider y as a constant. e'll need the Product Rule here, and also the Chain Rule...

3. Andresfon12

|dw:1361122439795:dw|

4. Andresfon12

fx = 1/ (cos x)* -sin (x)

take ln on both sides.

6. Andresfon12

7. ZeHanz

I understand what you wrote in a) now ;) $\frac{ \delta z }{ \delta y }=2e^{x+2y}\sin y+e^{x+2y} \cos y=e^{x+2y}(2\sin y + \cos y)$Now set x = 1 and y = ½: $\frac{ \delta z }{ \delta y }(1,\frac{ 1 }{ 2 })=e^{2}(2\sin 1+\cos \frac{ 1 }{ 2 })$

8. ZeHanz

Second one: f(x, y) = x ln(ycos x). I need fx, so y is constant:$\frac{ \delta f }{ \delta x }=1 \cdot \ln(y \cos x)+x \cdot \frac{ 1 }{ y \cos x }\cdot -y \sin x=\ln(y \cos x)- x \tan x$Now set x = pi/3, y = 1:$\ln(\cos \frac{ \pi }{ 3 })-\frac{ \pi }{ 3 }\tan \frac{ \pi }{ 3 }=\ln \frac{ 1 }{ 2 }-\frac{ \pi }{ 3 }\sqrt{3}=-(\ln2+\frac{ \pi }{ 3 }\sqrt{3})$