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Cálculo de funciones derivadas (1)

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