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

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

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

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

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derivative of

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)

y^{^{'}} + \frac{2 y}{x} = - \frac{2}{x}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 6 y = 0

\frac{d}{d x} (\frac{x - y}{2 x + 4 y})

y - 3 ln (x) - 4 = 0

\int e^{7 x + 6} d x

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