What is the derivative of (cos(mx)/(sin(nx))) ?

The derivative of (cos(mx)/(sin(nx))) is -msin(mx)csc(nx)-ncot(nx)csc(nx)cos(mx)

What is the first derivative of (cos(mx)/(sin(nx))) ?

The first derivative of (cos(mx)/(sin(nx))) is -msin(mx)csc(nx)-ncot(nx)csc(nx)cos(mx)

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\frac{d}{d x} (\frac{cos ( m x )}{sin ( n x )})

- m sin (m x) csc (n x) - n cot (n x) csc (n x) cos (m x)

Solution steps

\frac{d}{d x} (\frac{cos ( m x )}{sin ( n x )})

Simplify

\frac{cos ( m x )}{sin ( n x )} : cos (m x) csc (n x)

= \frac{d}{d x} (cos (m x) csc (n x))

Apply the Product Rule:

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

f = cos (m x), g = csc (n x)

= \frac{d}{d x} (cos (m x)) csc (n x) + \frac{d}{d x} (csc (n x)) cos (m x)

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

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

= (- sin (m x) m) csc (n x) + (- cot (n x) csc (n x) n) cos (m x)

Simplify

= - m sin (m x) csc (n x) - n cot (n x) csc (n x) cos (m x)

\int_{0}^{4} (9 e^{- 2 x}) d x

\int \frac{4}{100 - t} d t

\frac{d}{d x} ((5 + x) ln (x))

x + 1, 0.75

y = e^{x}, y = e^{- 2 x}, x = ln (5)

What is the derivative of (cos(mx)/(sin(nx))) ?
The derivative of (cos(mx)/(sin(nx))) is -msin(mx)csc(nx)-ncot(nx)csc(nx)cos(mx)
What is the first derivative of (cos(mx)/(sin(nx))) ?
The first derivative of (cos(mx)/(sin(nx))) is -msin(mx)csc(nx)-ncot(nx)csc(nx)cos(mx)