What is the derivative of f(x)=2tan^2(6x) ?

The derivative of f(x)=2tan^2(6x) is 24sec^2(6x)tan(6x)

What is the first derivative of f(x)=2tan^2(6x) ?

The first derivative of f(x)=2tan^2(6x) is 24sec^2(6x)tan(6x)

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derivative of

f (x) = 2 tan^{2} (6 x)

24 sec^{2} (6 x) tan (6 x)

Solution steps

\frac{d}{d x} (2 tan^{2} (6 x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (tan^{2} (6 x))

Apply the chain rule:

2 tan (6 x) \frac{d}{d x} (tan (6 x))

= 2 tan (6 x) \frac{d}{d x} (tan (6 x))

\frac{d}{d x} (tan (6 x)) = sec^{2} (6 x) \cdot 6

= 2 \cdot 2 tan (6 x) sec^{2} (6 x) \cdot 6

Simplify

= 24 sec^{2} (6 x) tan (6 x)

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What is the derivative of f(x)=2tan^2(6x) ?
The derivative of f(x)=2tan^2(6x) is 24sec^2(6x)tan(6x)
What is the first derivative of f(x)=2tan^2(6x) ?
The first derivative of f(x)=2tan^2(6x) is 24sec^2(6x)tan(6x)