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

The derivative of 1/(cos(x)+1/(sin(x+1))) is sec(x)tan(x)-cot(x+1)csc(x+1)

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

The first derivative of 1/(cos(x)+1/(sin(x+1))) is sec(x)tan(x)-cot(x+1)csc(x+1)

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

sec (x) tan (x) - cot (x + 1) csc (x + 1)

Solution steps

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

Simplify

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

= \frac{d}{d x} (sec (x) + csc (x + 1))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (sec (x)) + \frac{d}{d x} (csc (x + 1))

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

\frac{d}{d x} (csc (x + 1)) = - cot (x + 1) csc (x + 1)

= sec (x) tan (x) - cot (x + 1) csc (x + 1)

\frac{d}{d θ} (\frac{e ^{i θ} + e ^{- i θ}}{2})

y = \frac{t - t}{t ^{\frac{1}{3}}}

\int \frac{4 x + 5}{x ^{2} + 1} d x

\frac{d}{d x} (x^{2} \cdot e^{4 x})

\int 3 x - 6 x d x

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