Calcula la función derivada de:
(a) f(x)=x^{6} (e) f(x)=\dfrac{1}{x^{3}}
(b) f(x)=\sqrt{2} (f) f(x)=\sqrt{x}
(c) f(x)=\dfrac{1}{x} (g) f(x)=\pi
(d) f(x)=x (h) f(x)=3x
Resolución:
(a) f(x)=x^{6} f^{'}(x)=6x^{5}
(b) f(x)=\sqrt{2} f^{'}(x)=0
(c) f(x)=\dfrac{1}{x}=x^{-1} f^{'}(x)=-1x^{-2}=\dfrac{-1}{x^{2}}
(d) f(x)=x f^{'}(x)=1
(e) f(x)=\dfrac{1}{x^{3}}=x^{-3} f^{'}(x)=-3x^{-4}=\dfrac{-3}{x^{4}}
(f) f(x)=\sqrt{x}=x^{\frac{1}{2}} f^{'}(x)=\dfrac{1}{2}x^{\frac{1}{2}-1}=\dfrac{1}{2}x^{-\frac{1}{2}}=\dfrac{1}{2x^{\frac{1}{2}}}=\dfrac{1}{2\sqrt{x}}
(g) f(x)=\pi f^{'}(x)=0
(h) f(x)=3x f^{'}(x)=3