Is this right? (Chain Rule - Calc I)

1. Oct 17, 2012

Find the derivative of 101-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?

2. Oct 17, 2012

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?

3. Oct 17, 2012

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'