Find the partial derivative of z w.r.t. s:

z=e^r * cos(k)

where r = st and
k = sqrt{s^2+t^2}

Question

Find the partial derivative of z w.r.t. s:

z=e^r * cos(k)

where  r = st                            and
          k = sqrt{s^2+t^2}

anonymous · Answer

Let's put the value of r and k
$$z=e^{st}\times \cos (\sqrt {s^2+t^2})$$
Treat every variable other than s as constant
$$\frac{dz}{ds}=\cos (\sqrt {s^2+t^2})\frac d {ds} e^{st}+e^{st}\frac{d}{ds}\cos (\sqrt {s^2+t^2})$$
Can you try @taljaards ?

anonymous · Answer

$$\frac{dz}{ds} = \cos(\sqrt{s^2+t^2}) \times s - e^{st}\sin(\sqrt{s^2+t^2}) \times 0.5(s^2+t^2)^{-0.5}2t$$ ?

anonymous · Answer

derivative of st is t

aravindg · Answer

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anonymous · Answer

Hi!

Thanks for the help!

I'm glad I studied hard for the test - a similar question to this was actually asked!