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Popular >

derivative of csc(x-cot(x))

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

- cot (x) csc (x) - (- csc^{2} (x)) : \frac{1}{1 + cos ( x )}

= \frac{1}{1 + cos ( x )}

Graph

Popular Examples

integral of (18x+4)(9x^2+4x)^5

\int (18 x + 4) (9 x^{2} + 4 x)^{5} d x

(\partial)/(\partial x)(-4y^5sin(4x))

\frac{\partial}{\partial x} (- 4 y^{5} sin (4 x))

(\partial)/(\partial x)(7x^5y^7+3x^8y^6)

\frac{\partial}{\partial x} (7 x^{5} y^{7} + 3 x^{8} y^{6})

tangent of f(x)=4(x-1/x)^4,\at x=2 tangent of

f (x) = 4 (x - \frac{1}{x})^{4}, at x = 2

sum from n=1 to infinity of 1/(6n)

n = 1 \sum \infty \frac{1}{6 n}

Frequently Asked Questions (FAQ)

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