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Popular >

derivative of (cos(x)/(sec(x)))

Solution

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

Solution

- sin (2 x)

Solution steps

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

Simplify

\frac{cos ( x )}{sec ( x )} : cos^{2} (x)

= \frac{d}{d x} (cos^{2} (x))

Apply the chain rule:

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

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

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

= 2 cos (x) (- sin (x))

Simplify

2 cos (x) (- sin (x)) : - sin (2 x)

= - sin (2 x)

Popular Examples

integral of (e^{2x})/(1-e^x)

\int \frac{e ^{2 x}}{1 - e ^{x}} d x

derivative of ln((x+2/(x-1)))

\frac{d}{d x} (ln (\frac{x + 2}{x - 1}))

derivative of y=(x+2^x)/(cos(pix))derivative of

y = \frac{x + 2 ^{x}}{cos ( π x )}

derivative of ln(arctan(x))derivative of

ln (arctan (x))

(dy)/(dx)=2+1/x ,y(1)=5

\frac{d y}{d x} = 2 + \frac{1}{x}, y (1) = 5

Frequently Asked Questions (FAQ)

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