Chain Rule HW #1

Find the derivative of:  $y=\left(5x^3+3\right)^{4\ }$  

•  $y'=15x^2$  

•  $y'=15x^2\left(5x^{3\ }+3\right)^3$  

•  $y'=4\left(5x^{3\ }+3\right)^{3\ }$  

•  $y'=60x^2\left(5x^{3\ }+3\right)^{3\ }$  

Find the derivative of:  $y=\left(4x^5+5\right)^{\frac{1}{3}}$  

•  $\frac{dy}{dx}=\frac{20x^4}{\left(4x^5+5\right)^{\frac{2}{3}}}$  

•  $\frac{dy}{dx}=20x^4$  

•  $\frac{dy}{dx}=\frac{20x^{4\ }}{3\left(4x^5+5\right)^{\frac{2}{3}}}$  

•  $\frac{dy}{dx}=\frac{1}{3\left(4x^5+5\right)^{\frac{2}{3\ }}}$  

Find the derivative of:  $f\left(x\right)=\frac{1}{\left(-3x+1\right)^5}$  

•  $f'\left(x\right)=-\frac{3}{\left(-3x+1\right)^{6\ }}$  

•  $f'\left(x\right)=\frac{15}{\left(-3x+1\right)^6}$  

•  $f'\left(x\right)=-3$  

•  $f'\left(x\right)=-\frac{5}{\left(-3x+1\right)^6}$  

Find the derivative of:  $y=\left(-3x^4+2\right)^{4\ }$  

•  $y'=-12x^3\left(-3x^4+2\right)^3$  

•  $y'=4\left(-3x^4+2\right)^3$  

•  $y'=-48x^3\left(-3x^4+2\right)^3$  

•  $y'=-12x^3$