What is the derivative of y=3csc^2(5x)^3 ?

The derivative of y=3csc^2(5x)^3 is -90csc^6(5x)cot(5x)

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

The first derivative of y=3csc^2(5x)^3 is -90csc^6(5x)cot(5x)

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derivative of

y = 3 csc^{2} (5 x)^{3}

- 90 csc^{6} (5 x) cot (5 x)

Solution steps

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

Simplify

3 (csc^{2} (5 x))^{3} : 3 csc^{6} (5 x)

= \frac{d}{d x} (3 csc^{6} (5 x))

Take the constant out:

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

= 3 \frac{d}{d x} (csc^{6} (5 x))

Apply the chain rule:

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

= 6 (csc (5 x))^{5} \frac{d}{d x} (csc (5 x))

\frac{d}{d x} (csc (5 x)) = - cot (5 x) csc (5 x) \cdot 5

= 3 \cdot 6 (csc (5 x))^{5} (- cot (5 x) csc (5 x) \cdot 5)

Simplify

3 \cdot 6 csc^{5} (5 x) (- cot (5 x) csc (5 x) \cdot 5) : - 90 csc^{6} (5 x) cot (5 x)

= - 90 csc^{6} (5 x) cot (5 x)

What is the derivative of y=3csc^2(5x)^3 ?
The derivative of y=3csc^2(5x)^3 is -90csc^6(5x)cot(5x)
What is the first derivative of y=3csc^2(5x)^3 ?
The first derivative of y=3csc^2(5x)^3 is -90csc^6(5x)cot(5x)