What is the derivative of-1/2 cot^3(x) ?

The derivative of-1/2 cot^3(x) is 3/2 cot^2(x)csc^2(x)

What is the first derivative of-1/2 cot^3(x) ?

The first derivative of-1/2 cot^3(x) is 3/2 cot^2(x)csc^2(x)

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

\frac{3}{2} cot^{2} (x) csc^{2} (x)

Solution steps

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

Take the constant out:

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

= - \frac{1}{2} \frac{d}{d x} (cot^{3} (x))

Apply the chain rule:

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

= 3 (cot (x))^{2} \frac{d}{d x} (cot (x))

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

= - \frac{1}{2} \cdot 3 (cot (x))^{2} (- csc^{2} (x))

Simplify

- \frac{1}{2} \cdot 3 cot^{2} (x) (- csc^{2} (x)) : \frac{3}{2} cot^{2} (x) csc^{2} (x)

= \frac{3}{2} cot^{2} (x) csc^{2} (x)

\int - e^{y} d y

f (x) = ln (x) sin (x)

\frac{d}{d x} ((\frac{x - 6}{x + 7})^{3})

h \to + 0 lim (\frac{( 2 + h ) - 2}{h})

n = 0 \sum \infty \frac{n ^{2}}{n + 1}

What is the derivative of-1/2 cot^3(x) ?
The derivative of-1/2 cot^3(x) is 3/2 cot^2(x)csc^2(x)
What is the first derivative of-1/2 cot^3(x) ?
The first derivative of-1/2 cot^3(x) is 3/2 cot^2(x)csc^2(x)