The equation implicitly defines \( u \) as a function of \( x \). \( \quad-\frac{x^{2}}{u^{2}}-\cos (6 \mathrm{u})=-4 \) Find \( \frac{d u}{d x} \).

3. Encuentra la primera derivada por fórmula general. \( f(x)=3 x^{2}+11 x-8 \) \( f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} \)

Consider the parametric curve \( x=\cos \theta \) and \( y=\sin \theta \). Determine whether this curve is concave up, down, or neither at \( \theta=\frac{\pi}{6} \) A) upward B) downward C) neither D) All answers a b

1. Calcule la dorivada de les sisuiantos tunci a). \( f(x)=\left(3 x-x^{3}\right)^{100} \)

Evaluate the improper integral: \( \int_{1}^{\infty} \frac{1}{x^2} \, dx \)

Al resolver la integral doble \( \int_{1}^{2} \int_{1-x}^{\sqrt{x}} x^{2} y d y d x \) obtenemos: a. 402 b. 170 c. 170 d. \( 163 / 120 \)