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 differential calculus problems step by step online.
$\frac{\frac{d}{df}\left(fra\left(c^2t^2-1\right)\right)\left(t^3+t^2-2t\right)-fra\left(c^2t^2-1\right)\frac{d}{df}\left(t^3+t^2-2t\right)}{\left(t^3+t^2-2t\right)^2}$
Learn how to solve differential calculus problems step by step online. Find the derivative of (fra(c^2t^2-1))/(t^3+t^2-2t). 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 -(c^2t^2-1). The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=.