What is the derivative of (sin(5x)/(cos(6x))) ?

The derivative of (sin(5x)/(cos(6x))) is cos(5x)*5sec(6x)+sec(6x)tan(6x)*6sin(5x)

What is the first derivative of (sin(5x)/(cos(6x))) ?

The first derivative of (sin(5x)/(cos(6x))) is cos(5x)*5sec(6x)+sec(6x)tan(6x)*6sin(5x)

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\frac{d}{d x} (\frac{sin ( 5 x )}{cos ( 6 x )})

cos (5 x) \cdot 5 sec (6 x) + sec (6 x) tan (6 x) \cdot 6 sin (5 x)

Solution steps

\frac{d}{d x} (\frac{sin ( 5 x )}{cos ( 6 x )})

Simplify

\frac{sin ( 5 x )}{cos ( 6 x )} : sin (5 x) sec (6 x)

= \frac{d}{d x} (sin (5 x) sec (6 x))

Apply the Product Rule:

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

f = sin (5 x), g = sec (6 x)

= \frac{d}{d x} (sin (5 x)) sec (6 x) + \frac{d}{d x} (sec (6 x)) sin (5 x)

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

\frac{d}{d x} (sec (6 x)) = sec (6 x) tan (6 x) \cdot 6

= cos (5 x) \cdot 5 sec (6 x) + sec (6 x) tan (6 x) \cdot 6 sin (5 x)

\frac{d}{d x} ((x^{2} - 4)^{2} (x - 1))

\frac{( 1 - 5 t )}{2 + t}

\frac{\partial}{\partial x} (\frac{1}{2 π t} e^{- \frac{( x - y ) ^{2}}{2 t}})

x \to 1 - lim (2 x - 1)

f (x) = \frac{4 x}{x ^{2} + 4}

What is the derivative of (sin(5x)/(cos(6x))) ?
The derivative of (sin(5x)/(cos(6x))) is cos(5x)*5sec(6x)+sec(6x)tan(6x)*6sin(5x)
What is the first derivative of (sin(5x)/(cos(6x))) ?
The first derivative of (sin(5x)/(cos(6x))) is cos(5x)*5sec(6x)+sec(6x)tan(6x)*6sin(5x)