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Popular >

derivative of f(x)=sin(x)+1/2 cot(x)

Solution

derivative of

f (x) = sin (x) + \frac{1}{2} cot (x)

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (sin (x)) = cos (x)

\frac{d}{d x} (\frac{1}{2} cot (x)) = - \frac{1}{2} csc^{2} (x)

= cos (x) - \frac{1}{2} csc^{2} (x)

Graph

Popular Examples

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\int_{- 2}^{0} (2 + 4 - x^{2}) d x

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\int \frac{4 x - 11}{2 x ^{2} + 7 x - 4} d x

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

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x \to 0 lim (\frac{( a ^{x} - 1 )}{x})

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\int_{1}^{5} (x + 1)^{2} d x

Frequently Asked Questions (FAQ)

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