What is the derivative of sqrt(cos(4x)) ?

The derivative of sqrt(cos(4x)) is -2sin(4x)sqrt(sec(4x))

What is the first derivative of sqrt(cos(4x)) ?

The first derivative of sqrt(cos(4x)) is -2sin(4x)sqrt(sec(4x))

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\frac{d}{d x} (cos (4 x))

- 2 sin (4 x) sec (4 x)

Solution steps

\frac{d}{d x} (cos (4 x))

Apply the chain rule:

\frac{1}{2 cos ( 4 x )} \frac{d}{d x} (cos (4 x))

= \frac{1}{2 cos ( 4 x )} \frac{d}{d x} (cos (4 x))

\frac{d}{d x} (cos (4 x)) = - sin (4 x) \cdot 4

= \frac{1}{2 cos ( 4 x )} (- sin (4 x) \cdot 4)

Simplify

\frac{1}{2 cos ( 4 x )} (- sin (4 x) \cdot 4) : - 2 sin (4 x) sec (4 x)

= - 2 sin (4 x) sec (4 x)

\int \frac{2}{3 x + 5} d x

\int_{1}^{8} t ln (t) d t

\int_{0}^{4} x (0.5 - 0.125 x) d x

y^{^{''}} = 2

\frac{\partial}{\partial x} (K (x)^{\frac{1}{3}} L^{\frac{2}{3}})

What is the derivative of sqrt(cos(4x)) ?
The derivative of sqrt(cos(4x)) is -2sin(4x)sqrt(sec(4x))
What is the first derivative of sqrt(cos(4x)) ?
The first derivative of sqrt(cos(4x)) is -2sin(4x)sqrt(sec(4x))