What is the derivative of y = 10^(1-x^2)?

Jun 21, 2016

$y ' = - 2 \setminus \ln \left(10\right) \setminus x \setminus {10}^{1 - {x}^{2}}$ x

Explanation:

take natural logs

$\setminus \ln y = \setminus \ln \left({10}^{1 - {x}^{2}}\right) = \left(1 - {x}^{2}\right) \setminus \ln \left(10\right)$

$\setminus \setminus \frac{1}{y} y ' = - 2 x \setminus \ln \left(10\right)$

$y ' = - 2 x \setminus \ln 10 \setminus \times y = - 2 \setminus \ln \left(10\right) \setminus x \setminus {10}^{1 - {x}^{2}}$