Question

Find the derivative of the $sinx$ at $x=0$

• A. $1$
• B. $5$
• C. $3$
• D. $2$

Answer 1

Answer: (A)

Let $f(x)=sinx$. Then
$f^{\prime }(0)=\underset{h\to 0}{\lim }$ $\frac{f\left(0+h\right)-f\left(0\right)}{h}$
$=\underset{h\to 0}{\lim }$ $\frac{sin\left(0+h\right)-sin\left(0\right)}{h}$
$=\underset{h\to 0}{\lim }$ $\frac{sinh}{h}=1$