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Popular >

derivative of 2tan(cos(3x))

Solution

\frac{d}{d x} (2 tan (cos (3 x)))

Solution

- 6 sec^{2} (cos (3 x)) sin (3 x)

Solution steps

\frac{d}{d x} (2 tan (cos (3 x)))

Take the constant out:

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

= 2 \frac{d}{d x} (tan (cos (3 x)))

Apply the chain rule:

sec^{2} (cos (3 x)) \frac{d}{d x} (cos (3 x))

= sec^{2} (cos (3 x)) \frac{d}{d x} (cos (3 x))

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= 2 sec^{2} (cos (3 x)) (- sin (3 x) \cdot 3)

Simplify

= - 6 sec^{2} (cos (3 x)) sin (3 x)

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\int tan^{3} (θ) sec^{3} (θ) d θ

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Frequently Asked Questions (FAQ)

What is the derivative of 2tan(cos(3x)) ?
The derivative of 2tan(cos(3x)) is -6sec^2(cos(3x))sin(3x)
What is the first derivative of 2tan(cos(3x)) ?
The first derivative of 2tan(cos(3x)) is -6sec^2(cos(3x))sin(3x)