What is the derivative of cot^4(x-csc^4(x)) ?

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

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

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

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\frac{d}{d x} (cot^{4} (x) - csc^{4} (x))

4 csc^{2} (x) cot (x)

Solution steps

\frac{d}{d x} (cot^{4} (x) - csc^{4} (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (cot^{4} (x)) - \frac{d}{d x} (csc^{4} (x))

\frac{d}{d x} (cot^{4} (x)) = - 4 cot^{3} (x) csc^{2} (x)

\frac{d}{d x} (csc^{4} (x)) = - 4 csc^{4} (x) cot (x)

= - 4 cot^{3} (x) csc^{2} (x) - (- 4 csc^{4} (x) cot (x))

Simplify

- 4 cot^{3} (x) csc^{2} (x) - (- 4 csc^{4} (x) cot (x)) : 4 csc^{2} (x) cot (x)

= 4 csc^{2} (x) cot (x)

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