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 ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$
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Learn how to solve differential calculus problems step by step online. Find the derivative of (2sin(x)sin(y)-cos(x+y)cos(x-y))/(2cos(x)cos(y)). 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}}. The power of a product is equal to the product of it's factors raised to the same power. Simplify the product -(2\sin\left(x\right)\sin\left(y\right)-\cos\left(x+y\right)\cos\left(x-y\right)). The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.
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The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.