differentiate with respect to x

**orsonik** · November 16th 2007, 02:02 PM

(a) y = e^x ln x + x^3
Hint: Note that the first term on the right hand side is a
product of functions.
(b) y = e^2x^2
Hint: Use the chain–rule with u = 2x^2.

I have no clue how to solve these.help please is there a special equotation I have to use????

**topsquark** · November 16th 2007, 02:42 PM

Originally Posted by orsonik

(a) y = e^x ln x + x^3
Hint: Note that the first term on the right hand side is a
product of functions.
(b) y = e^2x^2
Hint: Use the chain–rule with u = 2x^2.

I have no clue how to solve these.help please is there a special equotation I have to use????

First note that
$\frac{d}{dx}e^x = e^x$

$\frac{d}{dx}ln(x) = \frac{1}{x}$

So
$y = e^x~ln(x) + x^3$

$\frac{dy}{dx} = \left ( \frac{d}{dx} e^x \right ) ln(x) + e^x \frac{d}{dx}ln(x) + \frac{d}{dx}x^3$

$\frac{dy}{dx} = e^x~ln(x) + e^x \cdot \frac{1}{x} + 3x^2$

For the second one:
$y = e^{2x^2}$

Let $f(u) = e^u$ and $u(x) = 2x^2$ .

So
$y = f(u(x))$

$\frac{dy}{dx} = \frac{df}{du} \cdot \frac{du}{dx}$

$\frac{dy}{dx} = e^{u(x)} \cdot 4x$

$\frac{dy}{dx} = 4x~e^{2x^2}$

-Dan

**orsonik** · November 16th 2007, 02:46 PM

oh my days. you are a real matematician magitian. I wish I was as good but I will probably never understand maths

((

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