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Popular Calculus >

derivative of tan(x-cot(x))

Solution

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

Solution

4 csc^{2} (2 x)

Solution steps

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

Simplify

tan (x) - cot (x) : - 2 cot (2 x)

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

= - 2 (- csc^{2} (2 x) \cdot 2)

Simplify

= 4 csc^{2} (2 x)

Graph

Popular Examples

integral of 4/(sin^2(x))

\int \frac{4}{sin ^{2} ( x )} d x

derivative of sin(narcsin(x))

\frac{d}{d x} (sin (n arcsin (x)))

integral of (8x-5)/(\sqrt[3]{x)}

\int \frac{8 x - 5}{3 x} d x

derivative of (sec(2x)/(1+tan(2x)))

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

integral of cot^3(x/3)

\int cot^{3} (\frac{x}{3}) d x

Frequently Asked Questions (FAQ)

What is the derivative of tan(x-cot(x)) ?
The derivative of tan(x-cot(x)) is 4csc^2(2x)
What is the first derivative of tan(x-cot(x)) ?
The first derivative of tan(x-cot(x)) is 4csc^2(2x)