{"id":472,"date":"2025-01-26T20:56:18","date_gmt":"2025-01-26T15:11:18","guid":{"rendered":"https:\/\/pokharelsugam.com.np\/bioinformatics\/?p=472"},"modified":"2025-01-27T15:40:40","modified_gmt":"2025-01-27T09:55:40","slug":"derivatives","status":"publish","type":"post","link":"https:\/\/pokharelsugam.com.np\/bioinformatics\/derivatives\/","title":{"rendered":"Derivatives"},"content":{"rendered":"\n<script type=\"text\/javascript\" async \n  src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-MML-AM_CHTML\">\n<\/script>\n\n\n\n<p class=\"has-medium-font-size\">Power Rule: \\( \\frac{d}{dx} \\left[ x^n \\right] = n x^{n-1} \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Constant Rule: \\( \\frac{d}{dx} \\left[ c \\right] = 0 \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Constant Multiple Rule: \\( \\frac{d}{dx} \\left[ k f(x) \\right] = k \\frac{d}{dx} f(x) \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Exponential Functions: <br>\\( \\frac{d}{dx} \\left[ e^x \\right] = e^x \\)<br>\\( \\frac{d}{dx} \\left[ e^{(ax+b)} \\right] = ae^{(ax+b)} \\)<br>\\( \\frac{d}{dx} \\left[ a^x \\right] = a^x \\ln a \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Logarithmic Functions:  <br>\\( \\frac{d}{dx} \\left[ \\ln x) \\right] = \\frac{1}{x} \\)<br>\\( \\frac{d}{dx} \\left[ \\log_a x \\right] = \\frac{1}{x \\ln a} \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Trigonometric Functions:<br>\\( \\frac{d}{dx} \\left[ \\sin(x) \\right] = \\cos(x) \\)<br>\\( \\frac{d}{dx} \\left[ \\cos(x) \\right] = -\\sin(x) \\)<br>\\( \\frac{d}{dx} \\left[ \\tan(x) \\right] = \\sec^2(x) \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\">\\( \\frac{d}{dx} \\left[ \\sin(ax \\pm b) \\right] = a\\cos(ax \\pm b) \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\">\\( \\frac{d}{dx} \\left[ \\csc(x) \\right] = -\\csc(x).\\cot(x) \\)<br>\\( \\frac{d}{dx} \\left[ \\sec(x) \\right] = \\sec(x).\\tan(x) \\)<br>\\( \\frac{d}{dx} \\left[ \\cot(x) \\right] = -\\csc^2(x) \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Sum\/Diff Rule: \\( \\frac{d}{dx} \\left[ u \\pm v \\right] = \\frac{du}{dx} \\pm \\frac{dv}{dx} \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Product Rule: \\( \\frac{d}{dx} \\left[ u.v \\right] = u \\frac{dv}{dx} + v \\frac{du}{dx}  \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Quotient Rule: \\( \\frac{d}{dx} \\left[ \\frac{u}{v} \\right] = \\frac{v \\frac{du}{dx} &#8211; u \\frac{dv}{dx}}{V^2} \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Chain Rule: \\( \\frac{dz}{dx} = \\frac{dz}{dy} \\times \\frac{dy}{dx} \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Inverse Trigonometric Functions:<br>\\( \\frac{d}{dx} \\left[ \\arcsin(x) \\right] = \\frac{1}{\\sqrt{1-x^2}} \\)<br>\\( \\frac{d}{dx} \\left[ \\arccos(x) \\right] = -\\frac{1}{\\sqrt{1-x^2}} \\)<br>\\( \\frac{d}{dx} \\left[ \\arctan(x) \\right] = \\frac{1}{1+x^2} \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Hyperbolic Functions:<br>\\( \\frac{d}{dx} \\left[ \\sinh(x) \\right] = \\cosh(x) \\)<br>\\( \\frac{d}{dx} \\left[ \\cosh(x) \\right] = \\sinh(x) \\)<br>\\( \\frac{d}{dx} \\left[ \\tanh(x) \\right] = \\text{sech}^2(x) \\)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Power Rule: \\( \\frac{d}{dx} \\left[ x^n \\right] = n x^{n-1} \\) Constant Rule: \\( \\frac{d}{dx} \\left[ c \\right] = 0 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center 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