7. (5 pts) Given that \( e^{y z}-x^{2}+2 x \sin z=0 \), find \( \frac{\partial z}{\partial x} \) using the implicit differentiation.

\( \int x \operatorname { arcsen } x d x \)

7. (5 pts) Given that \( e^{y=}-x^{2}+2 x \sin z=0 \), find \( \frac{\partial z}{\partial x} \) using the implicit differentiation. - This function has four critical points at

21. \( -\int(x-1)^{3} d x \) 22.- \( \int \frac{x}{x^{2}-1} d x \) 23.- \( \int \frac{4 x-3}{2 x^{2}-3 x-4} d x \) 24. \( -\int x^{2} \cdot e^{x^{3}} d x \) 25.- \( \int e^{2 x} d x \) 26. \( -\int 5^{3 x} d x \) 27. \( -\int \frac{\operatorname{sen} x}{5+e^{\cos x}} d x \) 28. \( -\int \sin 2 x d x \) 29.- \( \int x \cos x^{2} d x \) 30.- \( \int 4 \sin 5 x d x \)

Cargar el desarrollo paso a paso de la derivada de \( f(x)=\operatorname{Sen}^{2}\left(2 x^{3}\right) \) es

Let \( f(x)=4^{x} \) and \( g(x)=\left(\frac{1}{3}\right)^{x} \), and evaluate the following: \( \frac{f(x)-f(3)}{x-3}=\square \)