# Differentiation Problems

• Feb 27th 2009, 01:59 AM
tangehayes
Differentiation Problems
Hi,

I am in my late 20's and am going for an interview next week where I am required to do a maths test (arrgghh!) I havent done maths now in nearly 10 years but I was quite good at the time, but Im after forgetting all the principles now. I was wondering if you could give me some help on answering the questions below please - Id really appreciate it.

Differentiate the following:

f(x) = (x/x+1) 2(squared)

f(x) = -x +xlnx

f(x) = xe to the power of 2x + 10x
• Feb 27th 2009, 02:26 AM
earboth
Quote:

Originally Posted by tangehayes
...

Differentiate the following:

1) f(x) = (x/x+1) 2(squared)

2) f(x) = -x +xlnx

3) f(x) = xe to the power of 2x + 10x

to #1):
Use the chain rule with the quotient rule:

$\displaystyle f(x)=\left(\dfrac{x}{x+1}\right)^2~\implies~f'(x)= 2 \dfrac{x}{x+1} \cdot \dfrac{(x+1) \cdot 1 - x \cdot 1}{(x+1)^2} = \dfrac{2x}{(x+1)^3}$

to #2):
Use the product rule:

$\displaystyle f(x)=-x+x\cdot \ln(x)~\implies~ f'(x)=-1+\ln(x) \cdot 1+x\cdot \dfrac1x =\ln(x)$

to #3):
Please re-write the question: Use brackets to make clear what is an exponent, a factor, a summand, ...
• Feb 27th 2009, 03:03 AM
tangehayes
thank you so much, that is abolutely fantastic!

No 3:

$\displaystyle f(x)= xe^2x + 10x$

Its still not printing out properly (new to the math function) but it should bw xe to the power of 2x - hope you can make sense of this - thank you so much.
• Feb 27th 2009, 05:42 AM
earboth
Quote:

Originally Posted by tangehayes
thank you so much, that is abolutely fantastic!

No 3:

$\displaystyle f(x)= xe^{2x} + 10x$

Its still not printing out properly (new to the math function) but it should bw xe to the power of 2x - hope you can make sense of this - thank you so much.

1. Click on the equation in the quote to see how to type composed exponents.

2. Use product rule with chain rule:

$\displaystyle f(x)= xe^{2x} + 10x~\implies~f'(x)=e^{2x} \cdot 1 + x \cdot e^{2x} \cdot 2 + 10 = e^{2x}(2x+1)+10$