here are 2 differentiation problems which i need help on?

[ald942]

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

 

[galactus]

differentiate the following function:

$\displaystyle f(x) = ln(x^{2} - 4x + 4)$

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 $\displaystyle \frac{2x-4}{x^{2}-4x+4}=\frac{2(x-2)}{(x-2)^{2}}=\frac{2}{x-2}$

$\displaystyle f(x)= e^{x^{2}} + 1$

Chain rule again. Take derivative of x^2 and multiply it by $\displaystyle e^{x^{2}}$

We have $\displaystyle 2xe^{x^{2}}$