What is the d/(dt)((tan(t))/(cos(t)-4)) ?

The d/(dt)((tan(t))/(cos(t)-4)) is (sec^2(t)(cos(t)-4)+sin(t)tan(t))/((cos(t)-4)^2)

What is the first d/(dt)((tan(t))/(cos(t)-4)) ?

The first d/(dt)((tan(t))/(cos(t)-4)) is (sec^2(t)(cos(t)-4)+sin(t)tan(t))/((cos(t)-4)^2)

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\frac{d}{d t} (\frac{tan ( t )}{cos ( t ) - 4})

\frac{sec ^{2} ( t ) ( cos ( t ) - 4 ) + sin ( t ) tan ( t )}{( cos ( t ) - 4 ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{tan ( t )}{cos ( t ) - 4})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d t} ( tan ( t ) ) ( cos ( t ) - 4 ) - \frac{d}{d t} ( cos ( t ) - 4 ) tan ( t )}{( cos ( t ) - 4 ) ^{2}}

\frac{d}{d t} (tan (t)) = sec^{2} (t)

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

= \frac{sec ^{2} ( t ) ( cos ( t ) - 4 ) - ( - sin ( t ) ) tan ( t )}{( cos ( t ) - 4 ) ^{2}}

Simplify

= \frac{sec ^{2} ( t ) ( cos ( t ) - 4 ) + sin ( t ) tan ( t )}{( cos ( t ) - 4 ) ^{2}}

\int \frac{ln ( 11 x )}{x} d x

\int (x^{3})^{2} d x

f (x) = \frac{x ^{3} + 8}{x}

\int 4 + 4 x^{2} + x^{4} d x

\frac{6}{( s ^{2} \cdot ( s ^{2} + 8 s + 1 ) )}

What is the d/(dt)((tan(t))/(cos(t)-4)) ?
The d/(dt)((tan(t))/(cos(t)-4)) is (sec^2(t)(cos(t)-4)+sin(t)tan(t))/((cos(t)-4)^2)
What is the first d/(dt)((tan(t))/(cos(t)-4)) ?
The first d/(dt)((tan(t))/(cos(t)-4)) is (sec^2(t)(cos(t)-4)+sin(t)tan(t))/((cos(t)-4)^2)