What is the derivative of cot^3(pi-x) ?

The derivative of cot^3(pi-x) is 3csc^4(x)cos^2(x)

What is the first derivative of cot^3(pi-x) ?

The first derivative of cot^3(pi-x) is 3csc^4(x)cos^2(x)

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\frac{d}{d x} (cot^{3} (π - x))

3 csc^{4} (x) cos^{2} (x)

Solution steps

\frac{d}{d x} (cot^{3} (π - x))

Simplify

cot^{3} (π - x) : - \frac{cos ^{3} ( x )}{sin ^{3} ( x )}

= \frac{d}{d x} (- \frac{cos ^{3} ( x )}{sin ^{3} ( x )})

Take the constant out:

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

= - \frac{d}{d x} (\frac{cos ^{3} ( x )}{sin ^{3} ( x )})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= - \frac{\frac{d}{d x} ( cos ^{3} ( x ) ) sin ^{3} ( x ) - \frac{d}{d x} ( sin ^{3} ( x ) ) cos ^{3} ( x )}{( sin ^{3} ( x ) ) ^{2}}

\frac{d}{d x} (cos^{3} (x)) = - 3 cos^{2} (x) sin (x)

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

= - \frac{( - 3 cos ^{2} ( x ) sin ( x ) ) sin ^{3} ( x ) - 3 sin ^{2} ( x ) cos ( x ) cos ^{3} ( x )}{( sin ^{3} ( x ) ) ^{2}}

Simplify

- \frac{( - 3 cos ^{2} ( x ) sin ( x ) ) sin ^{3} ( x ) - 3 sin ^{2} ( x ) cos ( x ) cos ^{3} ( x )}{( sin ^{3} ( x ) ) ^{2}} : 3 csc^{4} (x) cos^{2} (x)

= 3 csc^{4} (x) cos^{2} (x)

x \to - 3 lim (\frac{1}{x - 1})

(- 2, 3), (2, - 2)

x \to 1 - lim (\frac{9}{x ^{3} - 1})

y^{^{'}} = \frac{( x ^{2} + y ^{2} )}{2 x y}

\frac{\partial}{\partial y} (\frac{1}{x + y ^{2}})

What is the derivative of cot^3(pi-x) ?
The derivative of cot^3(pi-x) is 3csc^4(x)cos^2(x)
What is the first derivative of cot^3(pi-x) ?
The first derivative of cot^3(pi-x) is 3csc^4(x)cos^2(x)