What is the derivative of (sin(4t))/(cos(6t)) ?

The derivative of (sin(4t))/(cos(6t)) is cos(4t)*4sec(6t)+sec(6t)tan(6t)*6sin(4t)

What is the first derivative of (sin(4t))/(cos(6t)) ?

The first derivative of (sin(4t))/(cos(6t)) is cos(4t)*4sec(6t)+sec(6t)tan(6t)*6sin(4t)

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derivative of

\frac{sin ( 4 t )}{cos ( 6 t )}

cos (4 t) \cdot 4 sec (6 t) + sec (6 t) tan (6 t) \cdot 6 sin (4 t)

Solution steps

\frac{d}{d t} (\frac{sin ( 4 t )}{cos ( 6 t )})

Simplify

\frac{sin ( 4 t )}{cos ( 6 t )} : sin (4 t) sec (6 t)

= \frac{d}{d t} (sin (4 t) sec (6 t))

Apply the Product Rule:

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

f = sin (4 t), g = sec (6 t)

= \frac{d}{d t} (sin (4 t)) sec (6 t) + \frac{d}{d t} (sec (6 t)) sin (4 t)

\frac{d}{d t} (sin (4 t)) = cos (4 t) \cdot 4

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

= cos (4 t) \cdot 4 sec (6 t) + sec (6 t) tan (6 t) \cdot 6 sin (4 t)

y = x^{3 x}

y^{^{''}} + y = sec (t)

n = 1 \sum \infty \frac{6 n}{9 - 2 n}

f (x) = (1 + x)^{- \frac{5}{3}}

\int x^{2} (6 x^{3} - 5)^{4} d x

What is the derivative of (sin(4t))/(cos(6t)) ?
The derivative of (sin(4t))/(cos(6t)) is cos(4t)*4sec(6t)+sec(6t)tan(6t)*6sin(4t)
What is the first derivative of (sin(4t))/(cos(6t)) ?
The first derivative of (sin(4t))/(cos(6t)) is cos(4t)*4sec(6t)+sec(6t)tan(6t)*6sin(4t)