Calcolare la derivata delle seguenti funzioni:

1) $\displaystyle y=-2$

2) $\displaystyle y=-2x$

3) $\displaystyle y=5x^3$

4) $\displaystyle y=\frac{4}{3}x^6$

5) $\displaystyle y=\sqrt[5]{x^{2}}$

6) $\displaystyle y=-2\ln x$

7) $\displaystyle y=7\cdot 3^x$

8) $\displaystyle y=5e^x$

9) $\displaystyle y=5\cos x$

10) $\displaystyle y=-3\sin x$

SOLUZIONE

1) $\displaystyle y’=0$

2) $\displaystyle y’=-2$

3) $\displaystyle y’=5\cdot 3x^2=15x^2$

4) $\displaystyle y’=\frac{4}{3}\cdot 6x^5=8x^5$

5) $\displaystyle y’=\frac{2}{5}x^{\frac{2}{5}-1}=\frac{2}{5}x^{-\frac{3}{5}}=\frac{2}{5 x^{\frac{3}{5}}}=\frac{2}{5\sqrt[5]{x^3}}$

6) $\displaystyle y’=-\frac{2}{x}$

7) $\displaystyle y’=7\cdot 3^x\ln 3$

8) $\displaystyle y’=5e^x$

9) $\displaystyle y’=5(-\sin x)=-5\sin x$

10) $\displaystyle y=-3\cos x$