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Popular >

derivative of cot(x+tan(x))

Solution

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

Solution

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

Solution steps

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

Simplify

cot (x) + tan (x) : 2 csc (2 x)

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

= - 4 cot (2 x) csc (2 x)

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\frac{d}{d x} (\frac{x ^{2} + x + 1}{x ^{2} + 3})

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\frac{d}{d x} ((2 - x + 3 x^{2}) (x^{3} + 5 e^{x}))

Frequently Asked Questions (FAQ)

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