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Any expression divided by one ($1$) is equal to that same expression
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$derivdef\left(\frac{\cos\left(x\right)\sin\left(x\right)}{\cos\left(x\right)}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of (cos(x)/1sin(x))/cos(x) using the definition. Any expression divided by one (1) is equal to that same expression. Simplify the fraction \frac{\cos\left(x\right)\sin\left(x\right)}{\cos\left(x\right)} by \cos\left(x\right). Find the derivative of \sin\left(x\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(x\right). Substituting f(x+h) and f(x) on the limit, we get. Using the sine of a sum formula: \sin(\alpha\pm\beta)=\sin(\alpha)\cos(\beta)\pm\cos(\alpha)\sin(\beta), where angle \alpha equals x, and angle \beta equals h.