A ald942 New member Joined Oct 4, 2009 Messages 8 Oct 4, 2009 #1 differentiate the following function: f(x) = ln(x squared - 4x + 4) differentiate the following function: f(x)= e to the power of x squared + 1 i would appreciateany help at all on these thanks
differentiate the following function: f(x) = ln(x squared - 4x + 4) differentiate the following function: f(x)= e to the power of x squared + 1 i would appreciateany help at all on these thanks
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,203 Oct 4, 2009 #2 differentiate the following function: \(\displaystyle f(x) = ln(x^{2} - 4x + 4)\) Click to expand... This is a standard differentiation problem, not an differential equation. Therefore, I moved it to calculus. Think chain rule. Derivative of inside times derivative of outside. \(\displaystyle \text{outside}=\frac{1}{x^{2}-4x+4}\) \(\displaystyle \text{inside}=2x-4\) Hence, we have \(\displaystyle \frac{2x-4}{x^{2}-4x+4}=\frac{2(x-2)}{(x-2)^{2}}=\frac{2}{x-2}\) \(\displaystyle f(x)= e^{x^{2}} + 1\) Click to expand... Chain rule again. Take derivative of x^2 and multiply it by \(\displaystyle e^{x^{2}}\) We have \(\displaystyle 2xe^{x^{2}}\)
differentiate the following function: \(\displaystyle f(x) = ln(x^{2} - 4x + 4)\) Click to expand... This is a standard differentiation problem, not an differential equation. Therefore, I moved it to calculus. Think chain rule. Derivative of inside times derivative of outside. \(\displaystyle \text{outside}=\frac{1}{x^{2}-4x+4}\) \(\displaystyle \text{inside}=2x-4\) Hence, we have \(\displaystyle \frac{2x-4}{x^{2}-4x+4}=\frac{2(x-2)}{(x-2)^{2}}=\frac{2}{x-2}\) \(\displaystyle f(x)= e^{x^{2}} + 1\) Click to expand... Chain rule again. Take derivative of x^2 and multiply it by \(\displaystyle e^{x^{2}}\) We have \(\displaystyle 2xe^{x^{2}}\)
