In the below image, on step 5, they have the formula: e^(-qt)*sqrt(T-t)* N'(d1)(d2/σ) Step 6, they adjust the bolded part to: e^(-qt)*sqrt(T-t)* N'(d1)(1-d1) and I can't seem to figure out how they did it. I'd be grateful if anyone had a little bit of knowledge they'd want to share. (I included the part about vega formula below this image and a link to the actual PDF as well.) https://acfr.aut.ac.nz/__data/assets/pdf_file/0017/185300/172496-K-Huang-Vanna-Volga_Auckland.pdf Cheers, NN