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$\frac{d}{dc}\left(c=\frac{\cos\left(5t\right)}{\sin\left(t\right)\cos\left(t\right)}\right)$
Learn how to solve problems step by step online. \frac{\cos \left(4\theta \right)}{\sin \left(\theta \right)}-\frac{\sin \left(4\theta \right)}{\cos \left(\theta \right)}=\frac{\cos \left(5\theta \right)}{\sin \left(\theta \right)\cos \left(\theta \right)}. Math interpretation of the question. Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the linear function is equal to 1. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}.