What is the derivative of sin(cos(tan(x))) ?

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

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

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

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derivative of

sin (cos (tan (x)))

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

Solution steps

\frac{d}{d x} (sin (cos (tan (x))))

Apply the chain rule:

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

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

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

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

Simplify

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

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