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Find the derivative of $\sin\left(2x\right)$ 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 $\sin\left(2x\right)$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
Multiply the single term $2$ by each term of the polynomial $\left(x+h\right)$
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$\lim_{h\to0}\left(\frac{\sin\left(2\left(x+h\right)\right)-\sin\left(2x\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of sin(2x) using the definition. Find the derivative of \sin\left(2x\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 \sin\left(2x\right). Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term 2 by each term of the polynomial \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).