Final answer to the problem
Step-by-step Solution
Specify the solving method
Find the derivative of $\arcsin\left(\frac{13}{50}\right)$ using the definition. Apply the definition of the derivative: $\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$. The function $f(x)$ is the function we want to differentiate, which is $\arcsin\left(\frac{13}{50}\right)$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
Learn how to solve definition of derivative problems step by step online.
$\lim_{h\to0}\left(\frac{\arcsin\left(\frac{13}{50}\right)-\arcsin\left(\frac{13}{50}\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of 2x+10=arcsin(13/50) using the definition. Find the derivative of \arcsin\left(\frac{13}{50}\right) using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is \arcsin\left(\frac{13}{50}\right). Substituting f(x+h) and f(x) on the limit, we get. Cancel like terms \arcsin\left(\frac{13}{50}\right) and -\arcsin\left(\frac{13}{50}\right). Zero divided by anything is equal to zero. The limit of a constant is just the constant.