Find the derivative using the product rule $\frac{d}{dx}\left(\frac{\sin\left(x\right)\left(3\sin\left(x\right)^2+2\cos\left(x\right)^2-4+2\cos\left(x\right)\right)}{8\left(1-\cos\left(x\right)\right)^{\frac{5}{2}}}\right)$
Unlock unlimited step-by-step solutions and much more!
Create a free account and unlock a glimpse of this solution.
Learn how to solve logarithmic differentiation problems step by step online. Find the derivative using the product rule d/dx((sin(x)(3sin(x)^2+2cos(x)^2+-42cos(x)))/(8(1-cos(x))^(5/2))). Simplifying. Simplifying. 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}}. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sin\left(x\right) and g=-1-\cos\left(x\right)^2+2\cos\left(x\right).
Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more