What is the derivative of (cos(3x)/(cos(x))) ?

The derivative of (cos(3x)/(cos(x))) is -3sin(3x)sec(x)+sec(x)tan(x)cos(3x)

What is the first derivative of (cos(3x)/(cos(x))) ?

The first derivative of (cos(3x)/(cos(x))) is -3sin(3x)sec(x)+sec(x)tan(x)cos(3x)

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\frac{d}{d x} (\frac{cos ( 3 x )}{cos ( x )})

- 3 sin (3 x) sec (x) + sec (x) tan (x) cos (3 x)

Solution steps

\frac{d}{d x} (\frac{cos ( 3 x )}{cos ( x )})

Simplify

\frac{cos ( 3 x )}{cos ( x )} : cos (3 x) sec (x)

= \frac{d}{d x} (cos (3 x) sec (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (3 x), g = sec (x)

= \frac{d}{d x} (cos (3 x)) sec (x) + \frac{d}{d x} (sec (x)) cos (3 x)

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

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

= (- sin (3 x) \cdot 3) sec (x) + sec (x) tan (x) cos (3 x)

Simplify

= - 3 sin (3 x) sec (x) + sec (x) tan (x) cos (3 x)

f (x) = e^{3 x}

\frac{5 ( 2 ) ^{2}}{3 ( 2 ) - 1}

x \to \infty lim (\frac{x}{7})

\frac{d}{d x} ((x^{20} - 22 x + 8) e^{x})

t x^{^{'}} + 4 x = 0

What is the derivative of (cos(3x)/(cos(x))) ?
The derivative of (cos(3x)/(cos(x))) is -3sin(3x)sec(x)+sec(x)tan(x)cos(3x)
What is the first derivative of (cos(3x)/(cos(x))) ?
The first derivative of (cos(3x)/(cos(x))) is -3sin(3x)sec(x)+sec(x)tan(x)cos(3x)