# Derivation and equations

• Apr 5th 2007, 12:32 AM
Vilkku
Derivation and equations
Hi !

I have two problems concerning computing the derivative and solving the equations. Just so the figures are correct I copied the problems from my PDF document and attached as word documentation with this message.

I hope that someone can help me !
• Apr 5th 2007, 02:47 AM
earboth
Quote:

Originally Posted by Vilkku
Hi !

I have two problems concerning computing the derivative and solving the equations. ...

Hello, Vilkku,

a) f'(x) = 12x³ + 4x^(-3)

b) Use quotient rule:
Code:

```        (3x-1)*1 - (x+2)*3      -7 f'(x) = ------------------- =  -----------               (3x-1)²            (3x-1)²```
c) Use product rule and chain rule

f'(x) = e^(3x)*2x + x²*e^(3x) * 3 = x*e^(3x)(2 + 3x)

d) Use chain rule:

f'(x) = 4(5x³ - x)³ * (15x² - 1)

Solve the equations:

a) e^(2x-1) = 3 <==> 2x-1 = ln(3) <==> x = ½(1 + ln(3))

b) 2^x - 15 = 0 <==> e^(x*ln(2)) = 15 <==> x*ln(2) = ln(15) <==> x = (ln(15))/(ln(2))

c) 50*1.05^(x) = 70 <==> e^(x*ln(1.05)) = 7/5 <==> x = (ln(7/5))/(ln(1.05))

EB