 # If y(x)=\sin u, then y' is Option 1:-\frac{du}{dx}\cos u Opt kuCAu 2021-10-04 Answered
If $$\displaystyle{y}{\left({x}\right)}={\sin{{u}}}$$, then y' is
Option 1:$$\displaystyle-{\frac{{{d}{u}}}{{{\left.{d}{x}\right.}}}}{\cos{{u}}}$$
Option 2:$$\displaystyle{\frac{{{d}{u}}}{{{\left.{d}{x}\right.}}}}{\cos{{u}}}$$
Option 3:$$\displaystyle{\cos{{u}}}$$
Option 4:$$\displaystyle-{\cos{{u}}}$$

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Step 1: To Find
Given, $$\displaystyle{y}{\left({x}\right)}={\sin{{u}}}$$, then we have to find y'.
Step 2: Calculation
Since we have $$\displaystyle{y}{\left({x}\right)}={\sin{{u}}}$$, then
$$\displaystyle{y}{\left({u}\right)}={\sin{{u}}}$$
diff. w.r. to u, we get
$$\displaystyle{y}'{\left({u}\right)}={\frac{{{d}}}{{{d}{u}}}}{\left({\sin{{u}}}\right)}$$
$$\displaystyle{y}'{\left({u}\right)}={\cos{{u}}}$$
Hence option (3) is correct.