Final answer to the problem
Step-by-step Solution
Specify the solving method
Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$
Learn how to solve problems step by step online.
$derivdef\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}\cos\left(x\right)\right)$
Learn how to solve problems step by step online. Find the derivative of tan(x)cos(x) using the definition. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Multiplying the fraction 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.