Question

Find the Derivative of Sin x.

• A. sin x
• B. cos x
• C. -cos x
• D. -sin x

Answer 1

The correct option is B

cos x

Let f(x)=sin x.

$f^{{}^{\prime }}\left(x\right)$ =$\underset{h\to 0}{lim}=\frac{sin(x+h)-sin\left(x\right)-sinx}{h}$

we know, $sinh\to 0andcosh\to 1ash\to D$

$=\underset{h\to 0}{lim}\frac{sinx(cosh-1)}{h}+\frac{sinhcosx}{h}$

Clearly$\left(\frac{cosh-1}{h}\right)\to 0ash\to 0$ [I hospitals Rules]

and$\frac{sinh}{h}\to ash\to 0$

$\therefore =\underset{h\to 0}{lim}\left(\frac{sinh}{h}\right)\left(cosx\right)=1\left(cosx\right)=cosx$

$\therefore Derivativeofsinx=cosx$