\( 7 y ^ { \prime \prime } - 2 \sqrt { 7 } y ^ { \prime } + y = 125 \cos ( \sqrt { 7 } x ) \)

3. \( h(x)=x^{2}+5 x-2 \) \( \frac{d h(x)}{d x}=\lim _{\Delta x \rightarrow}=\frac{h(x+\Delta x)-h(x)}{\Delta x} \)

Calcular \( y^{\prime}=\frac{d y}{d x} \) de la función implicit \( \frac{x^{2}}{4}+\frac{x^{2}}{9}=3 x y \) y simplificar:

\( \left. \begin{array} { l } { f ( x ) = - x ^ { 4 } - 3 x ^ { 3 } } \\ { h ( x ) = - 2 ( x - 2 ) ^ { 2 } ( x + 2 ) } \end{array} \right. \)

\( x^{3} y+y^{2}-x^{2}=5 \) Encuentra el valor de \( \frac{d y}{d x} \) en el punto \( (2,1) \)

Find the rate of change of total revenue, cost, and profit with respect to time. Assume that \( R(x) \) and \( C(x) \) are in doll \( R(x)=45 x-0.5 x^{2}, C(x)=4 x+10 \), when \( x=35 \) and \( \frac{d x}{d t}=20 \) units per day The rate of change of total revenue is \( \$ \square \) per day.