Derivative of e^cosx with Chain Rule | Calculus 1 Exercises

We differentiate e^cosx using the chain rule. The outside function f(x) is f(x) = e^x, and the inside function g(x) is g(x)=cosx. Then, f(g(x)) = e^cosx, so we see we've identified the outside and inside functions correctly. Applying the chain rule, we have the derivative of f(g(x)) is f'(g(x))*g'(x) = e(cosx)*(-sinx). #calculus1 #apcalculus Calculus 1 Exercises playlist:    • Calculus 1 Exercises   Calculus 1 playlist:    • Calculus 1   Chain Rule Explained:    • What is the Chain Rule? (Finding Derivativ...   Derivative of e^sinx:    • Derivative of e^sinx with Chain Rule | Cal...   Derivative of e^2x with Chain Rule:    • Derivative of e^2x (Chain Rule) | Calculus...   Derivative of e^3x with Chain Rule:    • Derivative of e^3x (Chain Rule) | Calculus...   Derivative of e^(1/x):    • Derivative of e^(1/x) with Chain Rule | Ca...   ◉Textbooks I Like◉ Graph Theory: https://amzn.to/3JHQtZj Real Analysis: https://amzn.to/3CMdgjI Abstract Algebra: https://amzn.to/3IjoZaO Linear Algebra: https://amzn.to/43xAWEz Calculus: https://amzn.to/3PieD1M Proofs and Set Theory: https://amzn.to/367VBXP (available for free online) Statistics: https://amzn.to/3tsaEER Discrete Math: https://amzn.to/3qfhoUn Number Theory: https://amzn.to/3JqpOQd ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits:   / wrathofmathlessons   ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Thanks to Loke Tan, Matt Venia, Micheline, Doug Walker, Odd Hultberg, Marc, Roslyn Goddard, Shlome Ashkenazi, Barbora Sharrock, Mohamad Nossier, Rolf Waefler, Shadow Master, and James Mead for their generous support on Patreon! Outro music is mine. You cannot find it anywhere, for now. Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu   My Math Rap channel:    / @mathbars2020