#### To determine

**To find:** The derivative of
y=cos(sec4x).

#### Answer

The derivative of
y=cos(sec4x) is
−4sin(sec4x)sec(4x)tan(4x).

#### Explanation

**Derivative Rules:**

**The Chain Rule:**

If *g* is differentiable at *x* and *f* is differentiable at
g(x), then the composite function
F=f∘g defined by
F(x)=f(g(x)) is differentiable at *x* and
F′ is given by the product

F′(x)=f′(g(x))⋅g′(x) (1)

**Calculation:**

Obtain the derivative of *y.*

y′=ddx(cos(sec4x))

Apply chain rule and simplify as,

y′=(−sin(sec4x))ddx(sec4x)

Apply chain rule once again and simplify as,

y′=(−sin(sec4x))ddx(sec4x)=(−sin(sec4x))(sec4xtan4x)ddx(4x)=−sin(sec4x)(sec4xtan4x)(4)=−4sin(sec4x)sec(4x)tan(4x)

Therefore, the derivative of
y=cos(sec4x) is
−4sin(sec4x)sec(4x)tan(4x).