What is the derivative of sin(tan(x)+sec(x)) ?

The derivative of sin(tan(x)+sec(x)) is -(cos(tan(x)+sec(x)))/(-1+sin(x))

What is the first derivative of sin(tan(x)+sec(x)) ?

The first derivative of sin(tan(x)+sec(x)) is -(cos(tan(x)+sec(x)))/(-1+sin(x))

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derivative of

sin (tan (x) + sec (x))

- \frac{cos ( tan ( x ) + sec ( x ) )}{- 1 + sin ( x )}

Solution steps

\frac{d}{d x} (sin (tan (x) + sec (x)))

Apply the chain rule:

cos (tan (x) + sec (x)) \frac{d}{d x} (tan (x) + sec (x))

= cos (tan (x) + sec (x)) \frac{d}{d x} (tan (x) + sec (x))

\frac{d}{d x} (tan (x) + sec (x)) = - \frac{1}{- 1 + sin ( x )}

= cos (tan (x) + sec (x)) (- \frac{1}{- 1 + sin ( x )})

Simplify

cos (tan (x) + sec (x)) (- \frac{1}{- 1 + sin ( x )}) : - \frac{cos ( tan ( x ) + sec ( x ) )}{- 1 + sin ( x )}

= - \frac{cos ( tan ( x ) + sec ( x ) )}{- 1 + sin ( x )}

What is the derivative of sin(tan(x)+sec(x)) ?
The derivative of sin(tan(x)+sec(x)) is -(cos(tan(x)+sec(x)))/(-1+sin(x))
What is the first derivative of sin(tan(x)+sec(x)) ?
The first derivative of sin(tan(x)+sec(x)) is -(cos(tan(x)+sec(x)))/(-1+sin(x))