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Popular >

derivative of (sin(x+cos(x))/(sin(x)))

Solution

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

Solution

- csc^{2} (x)

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (1) = 0

\frac{d}{d x} (cot (x)) = - csc^{2} (x)

= 0 - csc^{2} (x)

Simplify

= - csc^{2} (x)

Popular Examples

join (ax^2)/(ln(x/4))+(bx^4)/(x-4)join

\frac{a x ^{2}}{ln ( \frac{x}{4} )} + \frac{b x ^{4}}{x - 4}

(\partial)/(\partial x)(3x^2y^2-1)

\frac{\partial}{\partial x} (3 x^{2} y^{2} - 1)

maclaurin sqrt(x^2-1)maclaurin

x^{2} - 1

sum from n=2 to infinity of 1/(n(n+1))

n = 2 \sum \infty \frac{1}{n ( n + 1 )}

integral of x^{(-2)/3}sqrt(x^{1/3)-2}

\int x^{\frac{- 2}{3}} x^{\frac{1}{3}} - 2 d x

Frequently Asked Questions (FAQ)

What is the derivative of (sin(x+cos(x))/(sin(x))) ?
The derivative of (sin(x+cos(x))/(sin(x))) is -csc^2(x)
What is the first derivative of (sin(x+cos(x))/(sin(x))) ?
The first derivative of (sin(x+cos(x))/(sin(x))) is -csc^2(x)