Originally Posted by
chaneliman differentiate the following
y= e^(4x+1)*(x+1)^2 Use product and chain rules: $\displaystyle \color{red}\boxed{\frac{dy}{dx}=4e^{4x+1}(x+1)^2+2 e^{4x+1}(x+1)}$
y= e^(-4x)square root (x+1), x>-1 Again, use product and chain rules: $\displaystyle \frac{dy}{dx}=-4e^{-4x}\sqrt{x+1}+\frac{e^{-4x}}{2\sqrt{x+1}}=\color{red}\boxed{-\frac{(4x+3)e^{-4x}}{\sqrt{x+1}}}$
y= X^4 e^-2x Again, use product and chain rules: $\displaystyle \color{red}\boxed{\frac{dy}{dx}=4x^3e^{-2x}-2x^4e^{-2x}}$
y= (1/x)e^x Apply quotient rule: $\displaystyle \frac{dy}{dx}=\frac{xe^x-e^x}{e^{2x}}=\color{red}\boxed{\frac{x-1}{e^x}}$
(x^2 + 2x + 2)e^-x Use product and chain rules: $\displaystyle \frac{dy}{dx}=(2x+2)e^{-x}-(x^2+2x+2)e^{-x}=\color{red}\boxed{-x^2e^{-x}}$
Thanks