Why is the new format necessary before differentiating?

[PhysicsBoyMan]

Homework Statement

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Homework Equations

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The Attempt at a Solution

So I wanted to differentiate B(t) by saying

B(t) = P(t)(1.05)^20-t ln(1.05)

Apparently this is the wrong answer.

I'm supposed to change my function B(t) into this new form. From there I understand how they differentiated using the quotient rule. I can even understand how they got the new B(t) formula by splitting (1.05)²⁰ from (1.05)^-t, then changing that to 1/(1.05)^t and multiplying by P(t).
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What I don't understand is why my original attempt is wrong. Why is the new format necessary before we differentiate? It is because I have a negative exponent? Is it because I have two exponents?

Thanks for the help

 

[Mark44]

Homework Statement

[/PLAIN]
click image upload

Homework Equations

[/PLAIN]
free image upload

The Attempt at a Solution

So I wanted to differentiate B(t) by saying

B(t) = P(t)(1.05)^20-t ln(1.05)

Apparently this is the wrong answer.

B(t) is defined as a product, but it doesn't seem that you used the product rule.

I'm supposed to change my function B(t) into this new form. From there I understand how they differentiated using the quotient rule. I can even understand how they got the new B(t) formula by splitting (1.05)²⁰ from (1.05)^-t, then changing that to 1/(1.05)^t and multiplying by P(t).
[/PLAIN]
image hosting sites

What I don't understand is why my original attempt is wrong. Why is the new format necessary before we differentiate? It is because I have a negative exponent? Is it because I have two exponents?

Thanks for the help