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In this video, we'll explore the derivatives of exponential and hyperbolic functions, crucial concepts in calculus and mathematical analysis. We'll derive the formulas for the derivatives of exp(x), log(x), sinh(x), cosh(x), tanh(x), and their inverses. Topics Covered: - Derivatives of exponential functions (exp(x), log(x)) - Derivatives of hyperbolic functions (sinh(x), cosh(x), tanh(x)) and their co-ratios. Video Content: - Introduction to exponential and hyperbolic functions - Derivatives of exp(x) and log(x) - Derivatives of sinh(x), cosh(x), and tanh(x) and co-ratios. - Examples and practice problems - Visualizations and animations to illustrate key concepts Perfect for: - Students taking calculus, differential equations, or mathematical analysis courses - Researchers and professionals in physics, engineering, economics, and mathematics - Anyone interested in mathematical modeling and analysis Subscribe to our channel for more math and science content, and hit the notification bell to stay updated on our latest videos! #derivatives #derivative #differentiation #differentiation_class_12th #maths #mathematics #exponential #exponentialfunctions #derivativesoftheexponentialfunctions #hyperbolicfunctions #hyperbolic #derivativeofhyperbolicfunctions #calculus #12thclass #12thmaths #12thclassmath #fsc #fscpart2 #fscpart2math #ics #icsmaths #exercise #exercise2.6