How do you differentiate # f(x) = tan^2(3x)

#?

Question

How do you differentiate # f(x) = tan^2(3x)

#?

Ezra Adams · Accepted Answer

#If " f(x) = "tan^2(3x)#, then

#color(blue)((d)/(dx) f(x) = f'(x)=6 sec^2 (3x) * tan (3x)# Given: #f(x) = "tan^2(3x)# This function can be written as #f(x) = "tan(3x)^2# #d/(dx) tan(3x)^2# #rArr 2 tan (3x) (d/dx) tan (3x)# #rArr 2 *tan (3x) *Sec^2 (3x)*3# #rArr 6*sec^2(3x)*tan(3x)# Hence, #color(blue)((d)/(dx) f(x) = f'(x)= "6 sec^2 (3x) * tan (3x)#

Isaiah Allen · Answer

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This can also be written as:

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$$ f'(x) = 2\tan(3x)\sec^2(3x) $$

This can also be written as:

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\[ f'(x) = 2\tan(3x)\sec^2(3x) $$

This can also be written as:

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\[ f'(x) = 2\tan(3x)\sec^2(3x) $$

This can also be written as:

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\[ f'(x) = 2\tan(3x)\sec^2(3x) $$

This can also be written as:

$$ f'(x) = 2\tan(To differentiate $ f(x) = \tan^2(3x) $, you would use the chain rule. The derivative would be:

\[ f'(x) = 2\tan(3x)\sec^2(3x) \cdot 3 $$

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\[ f'(x) = 2\tan(3x)\sec^2(3x) $$

This can also be written as:

$$ f'(x) = 2\tan(3To differentiate $ f(x) = \tan^2(3x) $, you would use the chain rule. The derivative would be:

\[ f'(x) = 2\tan(3x)\sec^2(3x) \cdot 3 $$

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\[ f'(x) = 2\tan(3x)\sec^2(3x) $$

This can also be written as:

$$ f'(x) = 2\tan(3x)(To differentiate $ f(x) = \tan^2(3x) $, you would use the chain rule. The derivative would be:

\[ f'(x) = 2\tan(3x)\sec^2(3x) \cdot 3 $$

$$ f'(x) = 6To differentiate $ f(x) = \tan^2(3x) $, use the chain rule:

\[ f'(x) = 2\tan(3x)\sec^2(3x) $$

This can also be written as:

$$ f'(x) = 2\tan(3x)(1To differentiate $ f(x) = \tan^2(3x) $, you would use the chain rule. The derivative would be:

\[ f'(x) = 2\tan(3x)\sec^2(3x) \cdot 3 $$

$$ f'(x) = 6\tTo differentiate $ f(x) = \tan^2(3x) $, use the chain rule:

\[ f'(x) = 2\tan(3x)\sec^2(3x) $$

This can also be written as:

$$ f'(x) = 2\tan(3x)(1 +To differentiate $ f(x) = \tan^2(3x) $, you would use the chain rule. The derivative would be:

\[ f'(x) = 2\tan(3x)\sec^2(3x) \cdot 3 $$

$$ f'(x) = 6\tanTo differentiate $ f(x) = \tan^2(3x) $, use the chain rule:

\[ f'(x) = 2\tan(3x)\sec^2(3x) $$

This can also be written as:

$$ f'(x) = 2\tan(3x)(1 + \To differentiate $ f(x) = \tan^2(3x) $, you would use the chain rule. The derivative would be:

\[ f'(x) = 2\tan(3x)\sec^2(3x) \cdot 3 $$

$$ f'(x) = 6\tan(To differentiate $ f(x) = \tan^2(3x) $, use the chain rule:

\[ f'(x) = 2\tan(3x)\sec^2(3x) $$

This can also be written as:

$$ f'(x) = 2\tan(3x)(1 + \tanTo differentiate $ f(x) = \tan^2(3x) $, you would use the chain rule. The derivative would be:

\[ f'(x) = 2\tan(3x)\sec^2(3x) \cdot 3 $$

$$ f'(x) = 6\tan(3To differentiate $ f(x) = \tan^2(3x) $, use the chain rule:

\[ f'(x) = 2\tan(3x)\sec^2(3x) $$

This can also be written as:

$$ f'(x) = 2\tan(3x)(1 + \tan^To differentiate $ f(x) = \tan^2(3x) $, you would use the chain rule. The derivative would be:

\[ f'(x) = 2\tan(3x)\sec^2(3x) \cdot 3 $$

$$ f'(x) = 6\tan(3xTo differentiate $ f(x) = \tan^2(3x) $, use the chain rule:

\[ f'(x) = 2\tan(3x)\sec^2(3x) $$

This can also be written as:

$$ f'(x) = 2\tan(3x)(1 + \tan^2To differentiate $ f(x) = \tan^2(3x) $, you would use the chain rule. The derivative would be:

\[ f'(x) = 2\tan(3x)\sec^2(3x) \cdot 3 $$

$$ f'(x) = 6\tan(3x)\To differentiate $ f(x) = \tan^2(3x) $, use the chain rule:

\[ f'(x) = 2\tan(3x)\sec^2(3x) $$

This can also be written as:

$$ f'(x) = 2\tan(3x)(1 + \tan^2(To differentiate $ f(x) = \tan^2(3x) $, you would use the chain rule. The derivative would be:

\[ f'(x) = 2\tan(3x)\sec^2(3x) \cdot 3 $$

$$ f'(x) = 6\tan(3x)\sec^To differentiate $ f(x) = \tan^2(3x) $, use the chain rule:

\[ f'(x) = 2\tan(3x)\sec^2(3x) $$

This can also be written as:

$$ f'(x) = 2\tan(3x)(1 + \tan^2(3xTo differentiate $ f(x) = \tan^2(3x) $, you would use the chain rule. The derivative would be:

\[ f'(x) = 2\tan(3x)\sec^2(3x) \cdot 3 $$

$$ f'(x) = 6\tan(3x)\sec^2To differentiate $ f(x) = \tan^2(3x) $, use the chain rule:

\[ f'(x) = 2\tan(3x)\sec^2(3x) $$

This can also be written as:

$$ f'(x) = 2\tan(3x)(1 + \tan^2(3x))To differentiate $ f(x) = \tan^2(3x) $, you would use the chain rule. The derivative would be:

\[ f'(x) = 2\tan(3x)\sec^2(3x) \cdot 3 $$

$$ f'(x) = 6\tan(3x)\sec^2(3To differentiate $ f(x) = \tan^2(3x) $, use the chain rule:

\[ f'(x) = 2\tan(3x)\sec^2(3x) $$

This can also be written as:

$$ f'(x) = 2\tan(3x)(1 + \tan^2(3x)) $$To differentiate $ f(x) = \tan^2(3x) $, you would use the chain rule. The derivative would be:

$$ f'(x) = 2\tan(3x)\sec^2(3x) \cdot 3 $$

$$ f'(x) = 6\tan(3x)\sec^2(3xTo differentiate $ f(x) = \tan^2(3x) $, use the chain rule:

\[ f'(x) = 2\tan(3x)\sec^2(3x) $$

This can also be written as:

$$ f'(x) = 2\tan(3x)(1 + \tan^2(3x)) $$To differentiate $ f(x) = \tan^2(3x) $, you would use the chain rule. The derivative would be:

$$ f'(x) = 2\tan(3x)\sec^2(3x) \cdot 3 $$

$$ f'(x) = 6\tan(3x)\sec^2(3x)To differentiate $ f(x) = \tan^2(3x) $, use the chain rule:

\[ f'(x) = 2\tan(3x)\sec^2(3x) $$

This can also be written as:

$$ f'(x) = 2\tan(3x)(1 + \tan^2(3x)) $$To differentiate $ f(x) = \tan^2(3x) $, you would use the chain rule. The derivative would be:

$$ f'(x) = 2\tan(3x)\sec^2(3x) \cdot 3 $$

$$ f'(x) = 6\tan(3x)\sec^2(3x) $$