What is the derivative of (sin(2x)/(cos(3x))) ?

The derivative of (sin(2x)/(cos(3x))) is cos(2x)*2sec(3x)+sec(3x)tan(3x)*3sin(2x)

What is the first derivative of (sin(2x)/(cos(3x))) ?

The first derivative of (sin(2x)/(cos(3x))) is cos(2x)*2sec(3x)+sec(3x)tan(3x)*3sin(2x)

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\frac{d}{d x} (\frac{sin ( 2 x )}{cos ( 3 x )})

cos (2 x) \cdot 2 sec (3 x) + sec (3 x) tan (3 x) \cdot 3 sin (2 x)

Solution steps

\frac{d}{d x} (\frac{sin ( 2 x )}{cos ( 3 x )})

Simplify

\frac{sin ( 2 x )}{cos ( 3 x )} : sin (2 x) sec (3 x)

= \frac{d}{d x} (sin (2 x) sec (3 x))

Apply the Product Rule:

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

f = sin (2 x), g = sec (3 x)

= \frac{d}{d x} (sin (2 x)) sec (3 x) + \frac{d}{d x} (sec (3 x)) sin (2 x)

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

\frac{d}{d x} (sec (3 x)) = sec (3 x) tan (3 x) \cdot 3

= cos (2 x) \cdot 2 sec (3 x) + sec (3 x) tan (3 x) \cdot 3 sin (2 x)

x \to 0 lim (e^{(- 3 x)})

\frac{\partial}{\partial y} (7 - x^{2} - 2 y^{2})

\int \frac{x ^{5}}{( x ^{3} + 1 ) ( x ^{3} + 8 )} d x

\frac{( x ^{2} - 1 )}{x ^{2} + x + 1}

What is the derivative of (sin(2x)/(cos(3x))) ?
The derivative of (sin(2x)/(cos(3x))) is cos(2x)*2sec(3x)+sec(3x)tan(3x)*3sin(2x)
What is the first derivative of (sin(2x)/(cos(3x))) ?
The first derivative of (sin(2x)/(cos(3x))) is cos(2x)*2sec(3x)+sec(3x)tan(3x)*3sin(2x)