{"id":263860,"date":"2025-07-21T09:35:51","date_gmt":"2025-07-21T09:35:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=263860"},"modified":"2025-07-21T09:35:53","modified_gmt":"2025-07-21T09:35:53","slug":"determine-whether-each-of-the-following-statements-is-true-or-false-and-explain-why","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/21\/determine-whether-each-of-the-following-statements-is-true-or-false-and-explain-why\/","title":{"rendered":"Determine whether each of the following statements is true or false, and explain why"},"content":{"rendered":"\n

Determine whether each of the following statements is true or false, and explain why: The derivative of 10x is x10x-1.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The statement “The derivative of 10x is x10x-1” is false<\/strong>.<\/p>\n\n\n\n

To understand why, let’s break it down:<\/p>\n\n\n\n

    \n
  1. Derivative of a constant multiplied by a variable<\/strong>: The expression “10x” is a constant multiplied by the variable xxx, where 10 is a constant. The rule for differentiating such an expression is: ddx(c\u22c5xn)=c\u22c5n\u22c5xn\u22121\\frac{d}{dx}(c \\cdot x^n) = c \\cdot n \\cdot x^{n-1}dxd\u200b(c\u22c5xn)=c\u22c5n\u22c5xn\u22121 where ccc is a constant, and nnn is the exponent of xxx. In this case, the exponent of xxx is 1 (since 10x=10\u22c5x110x = 10 \\cdot x^110x=10\u22c5x1).<\/li>\n\n\n\n
  2. Applying the power rule<\/strong>: According to the power rule of differentiation, the derivative of x1x^1×1 is simply 1. So, applying this to 10x10x10x, we get: ddx(10x)=10\u22c51=10\\frac{d}{dx}(10x) = 10 \\cdot 1 = 10dxd\u200b(10x)=10\u22c51=10<\/li>\n<\/ol>\n\n\n\n

    Thus, the derivative of 10x10x10x is 10<\/strong>, not x10x\u22121x^{10x-1}x10x\u22121.<\/p>\n\n\n\n

    The expression “x10x-1” is not a valid representation of any simple derivative or algebraic simplification. It appears to be a misinterpretation or typographical error. Instead, the derivative of 10x10x10x is simply a constant, 10.<\/p>\n\n\n\n

    To summarize:<\/p>\n\n\n\n

      \n
    • The derivative of 10x10x10x is 10<\/strong>, not x10x\u22121x^{10x-1}x10x\u22121<\/li>\n<\/ul>\n\n\n\n
      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      Determine whether each of the following statements is true or false, and explain why: The derivative of 10x is x10x-1. The Correct Answer and Explanation is: The statement “The derivative of 10x is x10x-1” is false. To understand why, let’s break it down: Thus, the derivative of 10x10x10x is 10, not x10x\u22121x^{10x-1}x10x\u22121. The expression “x10x-1” […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"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":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-263860","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/263860","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=263860"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/263860\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=263860"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=263860"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=263860"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}