Question

If sin(xy)=x^2, then dy/dx =

Answer 1

implicit differentiation
for sin(xy)
differentiate and apply chain rule
\[{d\over dx}\sin(xy)=\cos(xy){d\over dx}(xy)\]

Answer 2

i did that and got \[\cos(xy)\times x \frac{ dy }{ dx } + y= 2x\]

Answer 3

that should be the thing on the left

Answer 4

\[{d\over dx}(xy)=x{dy\over dx}+y\]
this result multiplies with the cosine thingy

Answer 5

im still confused

Answer 6

ok..
\[
\cos(xy){d\over dx}(xy)=2x\\\text{but,}
{d\over dx}(xy)=x{dy\over dx}+y\\\text{so,}
\cos(xy)\left[x{dy\over dx}+y\right]=2x\\
x{dy\over dx}+y=2x\sec(xy)\\
x{dy\over dx}=2x\sec(xy)-y\\
{dy\over dx}=2\sec(xy)-{y\over x}
\]

Answer 7

oh!!! got it i