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Popular >

derivative of (1+cos(x)/(sin(x)))

Solution

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

Solution

- csc^{2} (x) - cot (x) csc (x)

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= - csc^{2} (x) - cot (x) csc (x)

Graph

Popular Examples

(\partial)/(\partial x)(3x-sqrt(3y^2+z^2))

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

integral of (x-e^{-x})^2

\int (x - e^{- x})^{2} d x

tangent of f(x)=(x^2)/(x-7)tangent of

f (x) = \frac{x ^{2}}{x - 7}

derivative of 5x-6

\frac{d}{d x} (5 x - 6)

integral of (x+15)/(x^2+16x+68)

\int \frac{x + 15}{x ^{2} + 16 x + 68} d x

Frequently Asked Questions (FAQ)

What is the derivative of (1+cos(x)/(sin(x))) ?
The derivative of (1+cos(x)/(sin(x))) is -csc^2(x)-cot(x)csc(x)
What is the first derivative of (1+cos(x)/(sin(x))) ?
The first derivative of (1+cos(x)/(sin(x))) is -csc^2(x)-cot(x)csc(x)