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Popular >

derivative of g(t)=tan(cos(2t))

Solution

derivative of

g (t) = tan (cos (2 t))

Solution

- 2 sec^{2} (cos (2 t)) sin (2 t)

Solution steps

\frac{d}{d t} (tan (cos (2 t)))

Apply the chain rule:

sec^{2} (cos (2 t)) \frac{d}{d t} (cos (2 t))

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

\frac{d}{d t} (cos (2 t)) = - sin (2 t) \cdot 2

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

Simplify

= - 2 sec^{2} (cos (2 t)) sin (2 t)

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Frequently Asked Questions (FAQ)

What is the derivative of g(t)=tan(cos(2t)) ?
The derivative of g(t)=tan(cos(2t)) is -2sec^2(cos(2t))sin(2t)
What is the first derivative of g(t)=tan(cos(2t)) ?
The first derivative of g(t)=tan(cos(2t)) is -2sec^2(cos(2t))sin(2t)