\( \frac{d}{dx}\frac{1}{sin^{2}x} \)

Calcula el área entre las curvas \( y = x^3 - 3x \) y \( y = x + 1 \) sobre el intervalo definido por sus intersecciones.

A solid is formed with triangular cross-sections where each triangle's base is defined by the equation \(y = x^2\) on interval \([0, 2]\). What is the volume of this solid?

Find the derivative of the function. \[ y=\frac{7}{x^{4}}-\frac{2}{x} \]

Use the fact that the derivative of the function \( g(x)=\sqrt{x} \) is \( g^{\prime}(x)=\frac{1}{2 \sqrt{x}} \) to find the equation of the tangent line to the graph of \( g(x) \) at the point \( x=81 \).

Find the derivative of the function. \( f(x)=-18 x^{\frac{3}{2}}+9 x^{1.3}+x \)