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Popular >

derivative of cot^4(x-csc^4(x))

Solution

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

Solution

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)

Graph

Popular Examples

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y = e^{in (x^{2} + 1)}

limit as x approaches 2 of (\sqrt[3]{3x^2-2x-8})/((x+2)^3)

x \to 2 lim (\frac{3 3 x ^{2} - 2 x - 8}{( x + 2 ) ^{3}})

limit as x approaches 9 of x-7

x \to 9 lim (x - 7)

taylor 1/((1+x^2))taylor

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

Frequently Asked Questions (FAQ)

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)