Question

find dy/dx by implicit differentiation 3cosxsiny=1

Answer 1

product rule is needed for the cos(x)*sin(y) part
chain rule is needed for the sin(y) part

Answer 2

\[3 \cdot [ \sin(y) \frac{d}{dx}(\cos(x))+\cos(x) \frac{d}{dx}( \sin(y))]=\frac{d}{dx}(1)\]

Answer 3

so easy question what is the derivative of (cos(x)) w.r.t x?

Answer 4

-sinx

Answer 5

ok so now we have
\[3[\sin(y)(-\sin(x))+\cos(x)\frac{d}{dx}(\sin(y))]=0 \]

Answer 6

last part for differentiating what is the derivative of sin(y) w.r.t x

Answer 7

cosy(y')

Answer 8

yep

Answer 9

\[3[-\sin(y)\sin(x)+\cos(x)\cos(y)y']=0 \]

Answer 10

now you can solve for y'
i suggest distributing the 3 first though

Answer 11

thanks so much these problems seem so scary at first but they are getting easier

Answer 12

cool stuff
they aren't too scary :)