What is the derivative of tan(5-sin(2x)) ?

The derivative of tan(5-sin(2x)) is -2sec^2(5-sin(2x))cos(2x)

What is the first derivative of tan(5-sin(2x)) ?

The first derivative of tan(5-sin(2x)) is -2sec^2(5-sin(2x))cos(2x)

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\frac{d}{d x} (tan (5 - sin (2 x)))

- 2 sec^{2} (5 - sin (2 x)) cos (2 x)

Solution steps

\frac{d}{d x} (tan (5 - sin (2 x)))

Apply the chain rule:

sec^{2} (5 - sin (2 x)) \frac{d}{d x} (5 - sin (2 x))

= sec^{2} (5 - sin (2 x)) \frac{d}{d x} (5 - sin (2 x))

\frac{d}{d x} (5 - sin (2 x)) = - 2 cos (2 x)

= sec^{2} (5 - sin (2 x)) (- 2 cos (2 x))

Simplify

= - 2 sec^{2} (5 - sin (2 x)) cos (2 x)

What is the derivative of tan(5-sin(2x)) ?
The derivative of tan(5-sin(2x)) is -2sec^2(5-sin(2x))cos(2x)
What is the first derivative of tan(5-sin(2x)) ?
The first derivative of tan(5-sin(2x)) is -2sec^2(5-sin(2x))cos(2x)