## Step-by-step solution

Problem to solve:

Solving method

Learn how to solve differential calculus problems step by step online.

$\lim_{h\to0}\left(\frac{\sin\left(2\left(x+h\right)\right)-\sin\left(2x\right)}{h}\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of sin(2*x). 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 \sin\left(2x\right). Substituting f(x+h) and f(x) on the limit. Solve the product 2\left(x+h\right). Using the sine of a sum formula: \sin(\alpha\pm\beta)=\sin(\alpha)\cos(\beta)\pm\cos(\alpha)\sin(\beta), where angle \alpha equals 2x, and angle \beta equals 2h. Factoring by \sin\left(2x\right).