Final answer to the problem
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 problems step by step online.
$\frac{\frac{d}{dx}\left(4x^2-5\sqrt[3]{x}+1\right)x-\left(4x^2-5\sqrt[3]{x}+1\right)\frac{d}{dx}\left(x\right)}{x^2}$
Learn how to solve problems step by step online. Find the derivative using the product rule d/dx((4x^2-5x^1/3+1)/x). 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}}. Simplify the product -(4x^2-5\sqrt[3]{x}+1). Simplify the product -(-5\sqrt[3]{x}+1). The derivative of the linear function is equal to 1.