Rubrica examen 1.4 - AIND - 4105.

 Encontrar la derivada de la siguiente función: $f\left(x\right)=Cos\left(-7x^6+12x^4-40\right)$ 

•  $\frac{\text{d}}{\text{d}y}f\left(x\right)=sen\left(-42x^5+48x^3\right)$  

•  $\frac{\text{d}}{\text{d}y}f\left(x\right)=\left(-42x^5+48x^3\right)sen\left(-7x^6+12x^4-40\right)$  

•  $\frac{\text{d}}{\text{d}y}f\left(x\right)=-\left(-42x^5+48x^3\right)sen\left(-7x^6+12x^4-40\right)$  

•  $\frac{\text{d}}{\text{d}y}f\left(x\right)=-\left(-42x^5+48x^3\right)\cos\left(-7x^6+12x^4-40\right)$  

 Suponiendo que a es un número real, encuentra la siguiente derivada: $f\left(x\right)=\ln\left(4a^3+5a^7\right)$ 

•  $\frac{\text{d}}{\text{d}y}f\left(x\right)=\frac{12}{4}$  

•  $\frac{\text{d}}{\text{d}y}f\left(x\right)=\frac{12a^2+35a^6}{4a^3+5a^7}$  

•  $\frac{\text{d}}{\text{d}y}f\left(x\right)=0$  

•  $\frac{\text{d}}{\text{d}y}f\left(x\right)=\frac{1}{4a^3+5a^7}$  

 $f\left(x\right)=\left(7x^5+12\right)\left(3x^2+11\right)$  

•  $\frac{\text{d}}{\text{d}y}f\left(x\right)=604x^{18}$  

•  $\frac{\text{d}}{\text{d}y}f\left(x\right)=105x^6+42x^5+385x^5+72x$  

•  $\frac{\text{d}}{\text{d}y}f\left(x\right)=105x^7+42x^6+385x^5+72x$  

•  $Ninguna\ de\ las\ opciones\ propuestas.$  

 Encontrar la derivada de la siguiente función: $f\left(x\right)=tg\left(3x^4+2x^2+3x\right)$ 

•  $\frac{\text{d}}{\text{d}y}f\left(x\right)=\sec\left(-42x^5+48x^3\right)$  

•  $\frac{\text{d}}{\text{d}y}f\left(x\right)=\left(12x^3+4x+3\right)\cos\left(3x^4+2x^2+3x\right)$  

•  $\frac{\text{d}}{\text{d}y}f\left(x\right)=-\left(-42x^5+48x^3\right)sen\left(-7x^6+12x^4-40\right)$  

•  $\frac{\text{d}}{\text{d}y}f\left(x\right)=\left(12x^3+4x+3\right)\sec^2\left(3x^4+2x^2+3x\right)$  

 Encontrar la derivada de la siguiente función: $f\left(x\right)=\sec\left(-11x^{-3}-7\right)$ 

•  $f\left(x\right)=33x^{-4}\sec\left(-11x^{-3}-7\right)tg\left(-11x^{-3}-7\right)$  

•  $f\left(x\right)=33x^{-4}\sec\left(-11x^{-3}-7\right)\sec\left(-11x^{-3}-7\right)$  

•  $f\left(x\right)=-33x^{-4}\sec\left(-11x^{-3}-7\right)tg\left(-11x^{-3}-7\right)$  

•  $f\left(x\right)=33x^4\sec\left(-11x^{-3}-7\right)tg\left(-11x^{-3}-7\right)$  

 $f\left(x\right)=\frac{2}{3}x^{\frac{7}{5}}-\frac{1}{4}x^{\frac{6}{11}}+\frac{4}{5}x^{\frac{8}{3}}$  

•  $f\left(x\right)=\frac{14}{15}x^{\frac{6}{5}}-\frac{6}{44}x^{-\frac{5}{11}}+\frac{32}{15}x^{\frac{5}{3}}$  

•  $f\left(x\right)=\frac{14}{15}x^{\frac{2}{5}}-\frac{6}{44}x^{-\frac{5}{11}}+\frac{32}{15}x^{\frac{5}{3}}$  

•  $f\left(x\right)=\frac{13}{15}x^{\frac{2}{5}}-\frac{6}{44}x^{-\frac{5}{11}}+\frac{3}{15}x^{\frac{5}{3}}$  

•  $f\left(x\right)=\frac{14}{3}x^{\frac{2}{5}}-\frac{7}{3}x^{-\frac{5}{11}}+\frac{8}{15}x^{\frac{5}{3}}$