Usando la regla del producto, calcule la derivada de : g(t) = [tex](t + \ frac{1}{t} )[ / tex] [tex](5t ^ {2} - \ frac{1}{t ^ {2} })[ / tex].
En resumen
<img src="https://tex.z-dn.net/?
<img src="https://tex.z-dn.net/?f=g%28t%29%3D%5Cbig%28t%2B%5Cfrac%7B1%7D%7Bt%7D%5Cbig%29%5Cbig%285t%5E2-%5Cfrac%7B1%7D%7Bt%5E2%7D%5Cbig%29%5C%5C%5C%5C%5Cfrac%7Bd%7D%7Bdt%7Dg%28t%29%3D%5Cbig%28t%2B%5Cfrac%7B1%7D%7Bt%7D%5Cbig%29%5Cfrac%7Bd%7D%7Bdt%7D%5Cbig%285t%5E2-%5Cfrac%7B1%7D%7Bt%5E2%7D%5Cbig%29%2B%5Cbig%285t%5E2-%5Cfrac%7B1%7D%7Bt%5E2%7D%5Cbig%29%5Cfrac%7Bd%7D%7Bdt%7D%5Cbig%28t%2B%5Cfrac%7B1%7D%7Bt%7D%5Cbig%29%5C%5C%5C%5C%5Cboxed%7B%5Cfrac%7Bd%7D%7Bdt%7Dg%28t%29%3D%5Cbig%28t%2B%5Cfrac%7B1%7D%7Bt%7D%5Cbig%29%5Cbig%2810t%2B%5Cfrac%7B2%7D%7Bt%5E3%7D%5Cbig%29%2B%5Cbig%285t%5E2-%5Cfrac%7B1%7D%7Bt%5E2%7D%5Cbig%29%5Cbig%281-%5Cfrac%7B1%7D%7Bt%5E2%7D%5Cbig%29%7D" />Simplificando : <img src="https://tex.z-dn.net/?f=%5Cbig%28t%2B%5Cfrac%7B1%7D%7Bt%7D%5Cbig%29%5Cbig%2810t%2B%5Cfrac%7B2%7D%7Bt%5E3%7D%5Cbig%29%2B%5Cbig%285t%5E2-%5Cfrac%7B1%7D%7Bt%5E2%7D%5Cbig%29%5Cbig%281-%5Cfrac%7B1%7D%7Bt%5E2%7D%5Cbig%29%5C%5C%5C%5C%3D%5Cfrac%7B2%281%2Bt%5E2%29%281%2B5t%5E4%29%7D%7Bt%5E4%7D%2B%5Cfrac%7B%28-1%2Bt%5E2%29%28-1%2B5t%5E4%29%7D%7Bt%5E4%7D%5C%5C%5C%5C%3D%5Cfrac%7B15t%5E6%2B5t%5E4%2Bt%5E2%2B3%7D%7Bt%5E4%7D%3D15t%5E2%2B5%2B%5Cfrac%7B1%7D%7Bt%5E2%7D%2B%5Cfrac%7B3%7D%7Bt%5E4%7D%5C%5C%5C%5C%5Cboxed%7B%5Cfrac%7Bd%7D%7Bdt%7Dg%28t%29%3D15t%5E2%2B5%2B%5Cfrac%7B1%7D%7Bt%5E2%7D%2B%5Cfrac%7B3%7D%7Bt%5E4%7D%7D" />.
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Y = {3}√Tan(x²) Recuerda que : ⁿ√a = ( a ) ^ ( 1 / n ) y = [ Tan(x²) ] ^ (1 / 3) Como hay tres funciones compuestas, aplicaremos la regla de la cadena : Algebraica → Trigonométrica → Algebraica x ^ (1 / 3) → Tan(x) → x²…