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))#