What is the derivative of (1+sin(x)/(cos(x))) ?

The derivative of (1+sin(x)/(cos(x))) is -1/(-1+sin(x))

What is the first derivative of (1+sin(x)/(cos(x))) ?

The first derivative of (1+sin(x)/(cos(x))) is -1/(-1+sin(x))

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\frac{d}{d x} (\frac{1 + sin ( x )}{cos ( x )})

- \frac{1}{- 1 + sin ( x )}

Solution steps

\frac{d}{d x} (\frac{1 + sin ( x )}{cos ( x )})

Simplify

\frac{1 + sin ( x )}{cos ( x )} : sec (x) + tan (x)

= \frac{d}{d x} (sec (x) + tan (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (sec (x)) + \frac{d}{d x} (tan (x))

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

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

= sec (x) tan (x) + sec^{2} (x)

Simplify

sec (x) tan (x) + sec^{2} (x) : - \frac{1}{- 1 + sin ( x )}

= - \frac{1}{- 1 + sin ( x )}

y^{^{'}} - \frac{4 y}{x} = - \frac{2}{x ^{2}}

\frac{- 6 x}{x ^{2} + 1}

\frac{d}{d y} (2 y^{3})

\int \frac{x ^{3} - 2}{x} d x

f (x) = \frac{1 - 2 t}{1 + 6 t}

What is the derivative of (1+sin(x)/(cos(x))) ?
The derivative of (1+sin(x)/(cos(x))) is -1/(-1+sin(x))
What is the first derivative of (1+sin(x)/(cos(x))) ?
The first derivative of (1+sin(x)/(cos(x))) is -1/(-1+sin(x))