- f′(x) = ln (cos 3x) − 3x tan 3x −3x^2
The rule for finding the derivative of y = ln u is , where u is a function of x.Here we will use the Product Rule to find the derivative: (−3 sin 3x) + (1) ln cos3 x − 3x^2 . This simplifies to f′(x) = ln (cos 3x) − 3x tan 3x − 3x^2.15.
The rule for finding the derivative of y = eu is , where u is a function of x. Herewe will use the Quotient Rule to find the derivative: f′(x) = . This can be simplified to
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16.
The rule for finding the derivative of y = loga u is , where u is a function of x.Before we find the derivative, we can use the laws of logarithms to expand the logarithm. Thisway, we won’t have to use the Product Rule or the Quotient Rule. We get f(x) = log 6 (3x tan x)= log 6 + x + log 6 tan x. Now we can find the derivative: f′(x) = 0 + . This can be simplified to .
17.
The rule for finding the derivative of y = loga u is , and the rule for finding thederivative of y = ln u is , where u is a function of x. Here we will use the Product