Find the derivative of the given function. \( f(x)=\tanh ^{-1}(4 x) \) \( f^{\prime}(x)=\square \)

10. El resultado de: A) \( 3 / 4 \operatorname{Ln}(4 x-6)+C \) B) \( 12 \operatorname{Ln}(4 x-6)+C \) C) \( 4 / 3 \operatorname{Ln}(4 x-6)+C \)\( \quad \int \frac{3}{4 x-6} d x \)

\( \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { \sqrt { 1 - x ^ { 2 } } } \sqrt { 1 - x ^ { 2 } - y ^ { 2 } } d y d x \)

Pregunta 11 Encuentra la derivada de la \( f(x)=\operatorname{Sen}(3 x) \) \( f^{\prime}(x)=\operatorname{Cos}(3 x) \) \( f^{\prime}(x)=\operatorname{Cos}(x) \) \( f^{\prime}(x)=3 x \operatorname{Cos}(3 x) \) \( f^{\prime}(x)=3 \operatorname{Cos}(3 x) \)

Use one or more definite integrals to find the area between the \( x \)-axis and the given curve on the given interval. Be sure to find if the curve crosses the \( x \)-axis in the given interval. \( f(x)=4 e^{x}-4 \) on \( [-2,2] \) Area:

\( \iint_{R} d A \), si \( R \) es la región, dada por: \[ R=\left\{(x, y) \in \mathbb{R}^{2}, 0 \leq x \leq \frac{1}{2}, y+x \leq 1, y \geq 0 .\right\} \]