Find the derivative of the function?

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Answer 1 · 2017-03-07T19:19:43

$dy/dx = -2ln(3)x(3^(9-x^2))$

Given: $y = 3^(9-x^2)$

Use the natural logarithm on both sides:

$ln(y) = ln(3^(9-x^2))$

Use the property $ln(a^b) = ln(a)(b)$ :

$ln(y) = ln(3)(9-x^2)$

Differentiate both sides:

$1/ydy/dx = -2ln(3)x$

Multiply both sides by y:

$dy/dx = -2ln(3)xy$

Substitute $3^(9-x^2)$ for y:

$dy/dx = -2ln(3)x(3^(9-x^2))$