# Math Help - Derivatives problem

1. ## Derivatives problem

I'm trying to differentiate the following..

$\frac{dG}{dz} = \frac{1-a}{1+a} * \frac{2a}{(1-az)^{2}}$

z is evaluated at 1 according to the Leibniz notation.

The answer is $\frac{2a}{1-a^2}$

I'm not quite sure how to get there.

$(1-az)^{-2}$ would be differentiated with the chain rule to give..

$-2(1-az)^{-3} * (-a) = \frac{2a}{(1-az)^{3}}$

Does the z disappear because we substitute in the value 1 at this point?

I'm not sure how to get rid of the (1+a) in the denominator.

2. Its already differentiated, can't you see?

dG/dz means that you already differendiated it. Now just substitute for z=1.

Now you got:

$\frac{dG}{dz} |_{z=1}= \frac{1-a}{1+a} * \frac{2a}{(1-a)^{2}}=\frac{1-a}{1+a}*\frac{2a}{(1-a)*(1-a)}=\frac{2a}{(1-a)*(1+a)}$
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9373171329498291, "perplexity": 1399.4672424678345}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936461612.31/warc/CC-MAIN-20150226074101-00222-ip-10-28-5-156.ec2.internal.warc.gz"}