Esercizi di matematica per le superiori/Derivate

Template:Quiz Template:Esercizi di matematica per le superiori <quiz display=simple> { Seleziona le derivate prime in x₀ = 2 corrette: |type="[]"} + $y=x+2\to y^{\prime }=1$ - $y=\frac{x+1}{x-1}\to y^{\prime }=-4$ - $y=\frac{\sqrt{2x}}{3}\to y^{\prime }=\frac{1}{3}$ - $y=\frac{\sqrt{x}}{2}\to y^{\prime }=\frac{\sqrt{2}}{2}$ + $y=e^x\to y^{\prime }=e^2$ - $y=\ln (x+3)\to y^{\prime }=\frac{1}{6}$ - $y=e^{x^2-1}\to y^{\prime }=e^2$ + $y=2\ln x\to y^{\prime }=1$ + $y=\sin x+\frac{\pi }{4}\to y^{\prime }=-\sin 2$ + $y=\frac{tanx}{x}\to y^{\prime }=\frac{1}{2}+\frac{\tan 2(2-1)}{4}$ - $y=2\to y^{\prime }=2$ </quiz>

2. Derivare le seguenti funzioni:

• $\frac{4}{3}x$
• $x^2+3x+3$
• $4x^3+5x^4-2x^2+x$
• $3x^{-2}-x^2$
• $\cos (5e^{\ln \frac{1}{5}x})$
• $\arctan (3x+\sin x)$
• $x^x$
• $x^5{e}^{x^3}\cos 3x$