Find the derivative using the product rule $\frac{d}{dx}\left(\frac{\left(5x^7\right)^{\frac{8}{3}}\sin\left(2x\right)}{\sqrt{2}+e^{3\cos\left(x\right)}}\right)$
Unlock unlimited step-by-step solutions and much more!
Create a free account and unlock a glimpse of this solution.
Learn how to solve problems step by step online. Find the derivative using the product rule d/dx(((5x^7)^(8/3)sin(2x))/(2^1/2+e^(3cos(x)))). Simplifying. The power of a product is equal to the product of it's factors raised to the same power. 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=\sqrt[3]{x^{56}} and g=73.100443\sin\left(2x\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