Derivative of 101-x2 using Chain Rule - Calculus I Explained

[UsernameValid]

Find the derivative of 10^1-x2.

1.) So, I used power rule to get: (1-x²)(10^-x2).
2.) Then I did chain rule and multiplied my previous answer with (d/dx)(-x²).
3.) The answer I get is: (-2x)(1-x²)(10^-x2).


When I use my calculator, the answer I get is: -20*ln(10)*10^-x2. So, where does -20*ln(10) come from?

 

[Muphrid]

The power rule applies when $x$ is the base, not in the exponent. What kinds of functions are the derivatives of the exponential function?

 

[Levi Tate]

You have to use the formula for a constant to a variable exponent..

a^u = lna (u) (u')

So you use properties of exponents to get 10 times 10 to the power of negative x squared..

So that's a constant with a variable exponent..

So you get 10(ln10)(10^-x^2)(-2x)
^u ^u'
Then that simplifies to your answer, but you forgot the x.

 

[UsernameValid]

Thanks! I understand it now. However, I've run into another problem: https://www.physicsforums.com/showthread.php?p=4119729#post4119729.