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

The derivative of (sin(2x)/(sin(3x))) is 2cos(2x)csc(3x)-3cot(3x)csc(3x)sin(2x)

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

The first derivative of (sin(2x)/(sin(3x))) is 2cos(2x)csc(3x)-3cot(3x)csc(3x)sin(2x)

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

2 cos (2 x) csc (3 x) - 3 cot (3 x) csc (3 x) sin (2 x)

Solution steps

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

Simplify

\frac{sin ( 2 x )}{sin ( 3 x )} : sin (2 x) csc (3 x)

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (csc (3 x)) = - cot (3 x) csc (3 x) \cdot 3

= cos (2 x) \cdot 2 csc (3 x) + (- cot (3 x) csc (3 x) \cdot 3) sin (2 x)

Simplify

= 2 cos (2 x) csc (3 x) - 3 cot (3 x) csc (3 x) sin (2 x)

ln (x) \frac{d y}{d x} = \frac{y}{x}

\frac{\partial}{\partial y} (e^{x} + x cos (y))

25 y^{^{''}} - 4 y = 0

e^{3 k}

\frac{d}{d x} ((3 x^{4} + 4 x)^{2} (5 x + 8)^{4})

What is the derivative of (sin(2x)/(sin(3x))) ?
The derivative of (sin(2x)/(sin(3x))) is 2cos(2x)csc(3x)-3cot(3x)csc(3x)sin(2x)
What is the first derivative of (sin(2x)/(sin(3x))) ?
The first derivative of (sin(2x)/(sin(3x))) is 2cos(2x)csc(3x)-3cot(3x)csc(3x)sin(2x)