Find the derivative of the function. Remember to use logarithmic properties before differentiating.
y = x(3^2x)
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y= u(x) v(x)
u(x) = x
v(x) = 3^2x
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u'(x) = 1
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y = a ^f (x)
y'= f '(x) a ^f (x) (ln a)
v(x) = 3^2x
v'(x) = 2 * 3^2x* ln (3)
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dy/ dx = u'(x)v(x) + u(x) v'(x)
dy/ dx = 1* 3^2x + x *2 * 3^2x* ln (3)
dy/ dx = 3^2x (1+2x* ln (3))
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Answer
dy/ dx = 3^2x (1+2x* ln (3))
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