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Popular >

derivative of sqrt(tan(x+cot(x)))

Solution

\frac{d}{d x} (tan (x) + cot (x))

Solution

- 2 cot (2 x) csc (2 x)

Solution steps

\frac{d}{d x} (tan (x) + cot (x))

Apply the chain rule:

\frac{1}{2 tan ( x ) + cot ( x )} \frac{d}{d x} (tan (x) + cot (x))

= \frac{1}{2 tan ( x ) + cot ( x )} \frac{d}{d x} (tan (x) + cot (x))

\frac{d}{d x} (tan (x) + cot (x)) = - 4 cot (2 x) csc (2 x)

= \frac{1}{2 tan ( x ) + cot ( x )} (- 4 cot (2 x) csc (2 x))

Simplify

\frac{1}{2 tan ( x ) + cot ( x )} (- 4 cot (2 x) csc (2 x)) : - 2 cot (2 x) csc (2 x)

= - 2 cot (2 x) csc (2 x)

Popular Examples

(\partial)/(\partial x)(sqrt(x^2+4xy+y^6))

\frac{\partial}{\partial x} (x^{2} + 4 x y + y^{6})

derivative of x/(2^x)

\frac{d}{d x} (\frac{x}{2 ^{x}})

integral from 1 to e of x^nln(x^m)

\int_{1}^{e} x^{n} ln (x^{m}) d x

(d^2)/(dx^2)(e^{6e^x})

\frac{d ^{2}}{d x ^{2}} (e^{6 e^{x}})

f(x)=x^4-4x^3-20x^2+96x+60

f (x) = x^{4} - 4 x^{3} - 20 x^{2} + 96 x + 60

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(tan(x+cot(x))) ?
The derivative of sqrt(tan(x+cot(x))) is -sqrt(2)cot(2x)sqrt(csc(2x))
What is the first derivative of sqrt(tan(x+cot(x))) ?
The first derivative of sqrt(tan(x+cot(x))) is -sqrt(2)cot(2x)sqrt(csc(2x))