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

The derivative of (y^2(csc(x))) is 2csc(x)y(dy)/(dx)-cot(x)csc(x)y^2

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

The first derivative of (y^2(csc(x))) is 2csc(x)y(dy)/(dx)-cot(x)csc(x)y^2

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\frac{d}{d x} ((y^{2}) (csc (x)))

2 csc (x) y \frac{d y}{d x} - cot (x) csc (x) y^{2}

Solution steps

\frac{d}{d x} ((y^{2}) (csc (x)))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y^{2}, g = csc (x)

= \frac{d}{d x} (y^{2}) csc (x) + \frac{d}{d x} (csc (x)) y^{2}

\frac{d}{d x} (y^{2}) = 2 y \frac{d y}{d x}

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

= 2 y \frac{d y}{d x} csc (x) + (- cot (x) csc (x)) y^{2}

Simplify

= 2 csc (x) y \frac{d y}{d x} - cot (x) csc (x) y^{2}

α^{2} + α y + αx + x y

i^{(25)}

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

[x^{2} + (3 x + 1)]^{2}

d - 1 - 9 d - 9

What is the derivative of (y^2(csc(x))) ?
The derivative of (y^2(csc(x))) is 2csc(x)y(dy)/(dx)-cot(x)csc(x)y^2
What is the first derivative of (y^2(csc(x))) ?
The first derivative of (y^2(csc(x))) is 2csc(x)y(dy)/(dx)-cot(x)csc(x)y^2