查看“︁微积分学/导数练习”︁的源代码

[[Wikibooks:首页|首页]] > [[Subject:索引|維基書架]] > [[数学书架]] > [[微积分学]] > '''导数练习'''

==求导数==
{|cellspacing=30
|valign=top|
<math>y=\frac {(2+5x)^{10}}{x}</math>

<math>
\begin{align}
y' & = \left[ \frac {(2+5x)^{10}}{x} \right]' \\
& = -\frac {1}{x^2}(2+5x)^{10} + \frac {1}{x}\cdot 10(2+5x)^9\cdot 5 \\
& = -\frac {(2+5x)^{10}}{x^2} + \frac {50(2+5x)^9}{x}
\end{align}
</math>
|valign=top|
<math>y=x\cos\left(2x+\frac{\pi}{2}\right)\sin\left(2x+\frac{\pi}{2}\right)</math>

<math>y  = x(-\sin2x)\cos2x = -\frac {1}{2}x\sin4x</math>

<math>
\begin{align}
y' & = \left(-\frac{1}{2}x\sin4x\right)' \\
& = -\frac{1}{2}\sin4x-\frac{1}{2}x\cos4x\cdot4 \\
& = -\frac{1}{2}\sin4x-2x\cos4x \\
\end{align}
</math>
|}
# 求下列函数的导数
## <math>\begin{align} f(x)=x^2+2x\\ \end{align}
</math>
## <math>f(x)=\sin(x^2)
</math>
## <math>f(x)=\sqrt{1-x^2}
</math>
## <math>f(x)=e^{x^{2}}
</math>
## <math>f(x)=\sin x\cos x
</math>

[[Category:數學分析]]