50. \( \int \frac{x d x}{3 x^{2}-4} \)

\( \frac { d } { d x } x ^ { 5 x } = \square \)

Compute the derivative. Use logarithmic differentiation where appropriate.

Hallar la derivada de la función \( f(x)=\operatorname{sen}\left(x^{2}-x\right) \)

Use the derivative \( f^{\prime}(x)=x^{2}(x-2)(x+2) \) to determine the local maxima and minima of \( f \) and the intervals of increase and decrease, Sketch a possible graph of \( f(f \) is not unique).

The following limit represents \( f^{\prime}(a) \) for some function \( f \) and some value a. a. Find the simplestrfunction \( f \) and a number \( a \). b. Determine the value of the limit by finding \( f^{\prime}(a) \). \( \lim _{x \rightarrow 1} \frac{x^{60}-1}{x-1} \)