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a/ ĐKXĐ:
\(sin\left(\frac{\pi}{2}.sinx\right)\ne0\Rightarrow\frac{\pi}{2}.sinx\ne k\pi\)
\(\Rightarrow sinx\ne2k\)
Mà \(-1\le sinx\le1\Rightarrow sinx\ne0\Rightarrow x\ne k\pi\)
b/
\(sinx-1\ge0\Leftrightarrow sinx\ge1\Rightarrow sinx=1\)
\(\Rightarrow x=\frac{\pi}{2}+k2\pi\)
c/
\(\left\{{}\begin{matrix}sinx\ne0\\cosx\ne0\\cos2x\ne0\end{matrix}\right.\) \(\Rightarrow sin4x\ne0\)
\(\Rightarrow x\ne\frac{k\pi}{4}\)
d/
\(\left\{{}\begin{matrix}sinx\ne0\\cosx\ne0\\sinx+cotx\ne0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}sin2x\ne0\\sin^2x+cosx\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x\ne k\pi\\-cos^2x+cosx+1\ne0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x\ne\frac{k\pi}{2}\\cosx\ne\frac{1-\sqrt{5}}{2}\\\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x\ne\frac{k\pi}{2}\\x\ne\pm arccos\left(\frac{1-\sqrt{5}}{2}\right)+k2\pi\end{matrix}\right.\)
e/
\(\left\{{}\begin{matrix}sinx\ne0\\cosx\ne1\end{matrix}\right.\) \(\Leftrightarrow sinx\ne0\Rightarrow x\ne k\pi\)
1: ĐKXĐ: 2x-1<>0
=>2x<>1
=>x<>1/2
=>TXĐ là D=R\{1/2}
2: ĐKXĐ: \(3x+\frac25\pi<>\frac{\pi}{2}+k\pi\)
=>\(3x<>\frac{\pi}{2}-\frac25\pi+k\pi=\frac{1}{10}\pi+k\pi\)
=>\(x<>\frac{1}{30}\pi+\frac{k\pi}{3}\)
=>TXĐ là D=R\{\(\frac{\pi}{30}+\frac{k\pi}{3}\) }
3: ĐKXĐ: \(2x-\frac13<>k\pi\)
=>\(2x<>\frac13+k\pi\)
=>\(x<>\frac16+\frac{k\pi}{2}\)
=>TXĐ là D=R\{\(\frac{k\pi}{2}+\frac16\) }
4: ĐKXĐ: sin x-cosx<>0
=>\(\sqrt2\cdot\sin\left(x-\frac{\pi}{4}\right)<>0\)
=>\(\sin\left(x-\frac{\pi}{4}\right)<>0\)
=>\(x-\frac{\pi}{4}<>k\pi\)
=>\(x<>\frac{\pi}{4}+k\pi\)
=>TXĐ là D=R\{\(\frac{\pi}{4}+k\pi\) }
5: ĐKXĐ: \(\begin{cases}\sin x<>0\\ cosx<>0\end{cases}\Rightarrow\begin{cases}x<>k\pi\\ x<>\frac{\pi}{2}+k\pi\end{cases}\Rightarrow x<>\frac{k\pi}{2}\)
=>TXĐ là D=R\{\(\frac{k\pi}{2}\) }
6: ĐKXĐ: \(\begin{cases}1-\sin x\ge0\\ cosx<>0\end{cases}\Rightarrow\begin{cases}\sin x<=1\\ x<>\frac{\pi}{2}+k\pi\end{cases}\)
=>\(x<>\frac{\pi}{2}+k\pi\)
=>TXĐ là D=R\{\(\frac{\pi}{2}+k\pi\) }
7: ĐKXĐ: \(\sin^2x-cos^2x<>0\)
=>\(cos^2x-\sin^2x<>0\)
=>cos2x<>0
=>\(2x<>\frac{\pi}{2}+k\pi\)
=>\(x<>\frac{\pi}{4}+\frac{k\pi}{2}\)
=>TXĐ là D=R\{\(\frac{\pi}{4}+\frac{k\pi}{2}\) }
8: ĐKXĐ: \(\begin{cases}x<>\frac{\pi}{2}+k\pi\\ \sin x<>-1\end{cases}\Rightarrow\begin{cases}x<>\frac{\pi}{2}+k\pi\\ x<>-\frac{\pi}{2}+k2\pi\end{cases}\)
=>\(x<>\frac{\pi}{2}+k\pi\)
=>TXĐ là D=R\{\(\frac{\pi}{2}+k\pi\) }
a.
\(y'=\dfrac{3}{cos^2\left(3x-\dfrac{\pi}{4}\right)}-\dfrac{2}{sin^2\left(2x-\dfrac{\pi}{3}\right)}-sin\left(x+\dfrac{\pi}{6}\right)\)
b.
\(y'=\dfrac{\dfrac{\left(2x+1\right)cosx}{2\sqrt{sinx+2}}-2\sqrt{sinx+2}}{\left(2x+1\right)^2}=\dfrac{\left(2x+1\right)cosx-4\left(sinx+2\right)}{\left(2x+1\right)^2}\)
c.
\(y'=-3sin\left(3x+\dfrac{\pi}{3}\right)-2cos\left(2x+\dfrac{\pi}{6}\right)-\dfrac{1}{sin^2\left(x+\dfrac{\pi}{4}\right)}\)
tham khảo:
a)\(y'=xsin2x+sin^2x\)
\(y'=sin^2x+xsin2x\)
b)\(y'=-2sin2x+2cosx\\ y'=2\left(cosx-sin2x\right)\)
c)\(y=sin3x-3sinx\)
\(y'=3cos3x-3cosx\)
d)\(y'=\dfrac{1}{cos^2x}-\dfrac{1}{sin^2x}\)
\(y'=\dfrac{sin^2x-cos^2x}{sin^2x.cos^2x}\)
a/ \(\left\{{}\begin{matrix}sin\left(1-x\right)\ne0\\cos\left(1-x\right)\ne0\end{matrix}\right.\) \(\Leftrightarrow sin\left(1-x\right).cos\left(1-x\right)\ne0\)
\(\Leftrightarrow sin\left(2-2x\right)\ne0\)
\(\Leftrightarrow2-2x\ne k\pi\Leftrightarrow x\ne1+\frac{k\pi}{2}\)
b và c bạn ghi như vầy ko biết mẫu số nằm ở đâu để tìm điều kiện
a/ \(x\in R\)
b/ \(x\ne0\)
c/ \(sin\left(3x+\frac{5\pi}{3}\right)\ne0\Leftrightarrow3x+\frac{5\pi}{3}\ne k\pi\)
\(\Leftrightarrow x\ne-\frac{5\pi}{9}+\frac{k\pi}{3}\)
d/ \(\left\{{}\begin{matrix}sinx\ne0\\sinx\ne1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ne k\pi\\x\ne\frac{\pi}{2}+k2\pi\end{matrix}\right.\)