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 quotient rule of differentiation problems step by step online.
$\frac{\frac{d}{dx}\left(\sqrt{x}-x^3\right)e^{5x}-\left(\sqrt{x}-x^3\right)\frac{d}{dx}\left(e^{5x}\right)}{\left(e^{5x}\right)^2}$
Learn how to solve quotient rule of differentiation problems step by step online. Find the derivative d/dx((x^1/2-x^3)/(e^(5x))). 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 \left(e^{5x}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 5x and n equals 2. Simplify the product -(\sqrt{x}-x^3). Applying the derivative of the exponential function.