Calcula la función derivada de:
(a) $f(x)=2x^{4}$
(b) $f(x)=x^{3}+3x^{2}+x+1$
(c) $f(x)=\dfrac{4}{x^{2}}$
(d) $f(x)=-7\sqrt[3]{x}$
(e) $f(x)=\dfrac{x^{2}}{5}$
Resolución:
(a) $f(x)=2x^{4}$ $f^{'}(x)=2·4x^{3}=8x^{3}$
(b) $f(x)=x^{3}+3x^{2}+x+1$ $f^{'}(x)=3x^{2}+6x+1$
(c) $f(x)=\dfrac{4}{x^{2}}=4x^{-2}$ $f^{'}(x)=-8x^{-3}=\dfrac{-8}{x^{3}}$
(d) $f(x)=-7\sqrt[3]{x}=-7x^{\frac{1}{3}}$ $f^{'}(x)=\dfrac{-7}{3}x^{\frac{1}{3}-1}=\dfrac{-7}{3}x^{-\frac{2}{3}}=\dfrac{-7}{3\sqrt[3]{x^{2}}}$
(e) $f(x)=\dfrac{x^{2}}{5}$ $f^{'}(x)=\dfrac{2}{5}x$
