Final Answer
Step-by-step Solution
Specify the solving method
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 ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$
Learn how to solve integrals with radicals problems step by step online.
$\frac{x^{199}\frac{d}{dx}\left(\sin\left(x\right)^{200}\right)\sin\left(4x\right)-\sin\left(x\right)^{200}\frac{d}{dx}\left(x^{199}\sin\left(4x\right)\right)}{\left(x^{199}\sin\left(4x\right)\right)^2}$
Learn how to solve integrals with radicals problems step by step online. Find the derivative of (sin(x)^200)/(sin(4x)x^199). 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. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sin\left(4x\right) and g=x^{199}. Simplify the product -(x^{199}\frac{d}{dx}\left(\sin\left(4x\right)\right)+\frac{d}{dx}\left(x^{199}\right)\sin\left(4x\right)).