im given the function f(r,a,b) and z=rcos(a) y=rsin(a)sin(b) x=rsin(a)cos(b)(adsbygoogle = window.adsbygoogle || []).push({});

now i need to find the partial derivative of f'_y, without solving r,a,b in terms of x,y,z, what that i got is:

f'_y=f'_a*a'_y+f'_r*r'_y+f'_b*b'_y

the answer should include the derivatives of f wrt r,a,b, which i think i did ok, (i only needed to calculate a'_y,b'_y,r'_y).

but i have another question and it's to solve r,a,b in terms of x,y,z which i did, and then to calculate the above derivative directly by the chain rule.

i think i need to use here a jacobian, so i defined the implicit functions: F=z-rcos(a) G=y-rsin(a)sin(b) H=x-rsin(a)cos(b), my proble is that in order to calclualte it: i need to know what's f, cause:

f'_y=-J((F,G,H)/(x,y,z))/J((F,G,H)/(x,f,z))

the question is how to do it?

thanks in advance.

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# Partial derivatives.

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