What is the derivative of f(x)=csc^3(5x^2+1) ?

The derivative of f(x)=csc^3(5x^2+1) is -30xcsc^3(5x^2+1)cot(5x^2+1)

What is the first derivative of f(x)=csc^3(5x^2+1) ?

The first derivative of f(x)=csc^3(5x^2+1) is -30xcsc^3(5x^2+1)cot(5x^2+1)

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derivative of

f (x) = csc^{3} (5 x^{2} + 1)

- 30 x csc^{3} (5 x^{2} + 1) cot (5 x^{2} + 1)

Solution steps

\frac{d}{d x} (csc^{3} (5 x^{2} + 1))

Apply the chain rule:

3 (csc (5 x^{2} + 1))^{2} \frac{d}{d x} (csc (5 x^{2} + 1))

= 3 (csc (5 x^{2} + 1))^{2} \frac{d}{d x} (csc (5 x^{2} + 1))

\frac{d}{d x} (csc (5 x^{2} + 1)) = - cot (5 x^{2} + 1) csc (5 x^{2} + 1) \cdot 10 x

= 3 (csc (5 x^{2} + 1))^{2} (- cot (5 x^{2} + 1) csc (5 x^{2} + 1) \cdot 10 x)

Simplify

3 csc^{2} (5 x^{2} + 1) (- cot (5 x^{2} + 1) csc (5 x^{2} + 1) \cdot 10 x) : - 30 x csc^{3} (5 x^{2} + 1) cot (5 x^{2} + 1)

= - 30 x csc^{3} (5 x^{2} + 1) cot (5 x^{2} + 1)

\int cot^{4} (\frac{1}{2}) t d t

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What is the derivative of f(x)=csc^3(5x^2+1) ?
The derivative of f(x)=csc^3(5x^2+1) is -30xcsc^3(5x^2+1)cot(5x^2+1)
What is the first derivative of f(x)=csc^3(5x^2+1) ?
The first derivative of f(x)=csc^3(5x^2+1) is -30xcsc^3(5x^2+1)cot(5x^2+1)