What is the derivative of f(x)=5csc^4(x) ?

The derivative of f(x)=5csc^4(x) is -20csc^4(x)cot(x)

What is the first derivative of f(x)=5csc^4(x) ?

The first derivative of f(x)=5csc^4(x) is -20csc^4(x)cot(x)

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derivative of

f (x) = 5 csc^{4} (x)

- 20 csc^{4} (x) cot (x)

Solution steps

\frac{d}{d x} (5 csc^{4} (x))

Take the constant out:

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

= 5 \frac{d}{d x} (csc^{4} (x))

Apply the chain rule:

4 (csc (x))^{3} \frac{d}{d x} (csc (x))

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

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

= 5 \cdot 4 (csc (x))^{3} (- cot (x) csc (x))

Simplify

5 \cdot 4 csc^{3} (x) (- cot (x) csc (x)) : - 20 csc^{4} (x) cot (x)

= - 20 csc^{4} (x) cot (x)

What is the derivative of f(x)=5csc^4(x) ?
The derivative of f(x)=5csc^4(x) is -20csc^4(x)cot(x)
What is the first derivative of f(x)=5csc^4(x) ?
The first derivative of f(x)=5csc^4(x) is -20csc^4(x)cot(x)