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