Derivatives seem ok but result is not as expected: pls help, can't complete the course for this!

[zahrafarajih]

Please, anyone has a hint about where to look for errors?

I made dfdmu as:

f(x, mu, sig) * (1/((sig**3) * (np.sqrt(2 * np.pi)))) * (x - mu)

dfdsig as:

f(x, mu, sig) * -(sig2 - x2 + 2mux - mu2)/(np.sqrt(2*np.pi) * sig4)

J = np.array([ -2*(y - f(x,mu,sig)) @ dfdmu(x,mu,sig),

    -2*(y - f(x,mu,sig)) @ dfdsig(x,mu,sig),])

I checked for errors in derivatives (by online calculator, too) and can't find any but the results are wrong.

Thanks in advance for your help!

[TheKidPadra]

Hi, zahra, if you still want to know why your original derivatives were wrong, here is a full explanation. It a mistake was made, it deserves to be investigated why it was a mistake. That's how progress is made.

df / dμ

I don't know what you got from the online derivative calculator, below is what I got by differentiate f with respect to μ by hands:

Hence, the partial derivative with respect to μ can be simplified to:

In Python, the partial derivative with respect to μ would look like:

def dfdmu (x,mu,sig) :
    return f(x, mu, sig) * (x-mu)/(sig**2)

Compare the above with your original code, which you stated in the post here, you would immediately know why your original answer was wrong.

df / dϬ

For the partial derivative with respect to б, the product rule is needed here:

Differentiate A(Ϭ) with respect to Ϭ and treat B(Ϭ) as constant for the moment.

Differentiate B(Ϭ) with respect to Ϭ and treat A(Ϭ) as constant now.

The partial derivative with respect to Ϭ is (1) + (2):Compare the above with your original code, which you stated in the post here, you would immediately know why your original answer was wrong.

df / dϬ

For the partial derivative with respect to б, the product rule is needed here:

Differentiate A(Ϭ) with respect to Ϭ and treat B(Ϭ) as constant for the moment.

Differentiate B(Ϭ) with respect to Ϭ and treat A(Ϭ) as constant now.

The partial derivative with respect to Ϭ is (1) + (2):

In Python, the partial derivative with respect to Ϭ would look like:

def dfdsig (x,mu,sig) :
    return f(x, mu, sig) * ((x-mu)**2/sig**3 - 1/sig)

Compare the above with your initial answer for df/dsig(x, mu, sig).

[zahrafarajih]

Thanks a lot TheKidPadra!
Going back to the basics helps and this is a wonderful explanation!