Differentiate the following function with respect of `x :(x^2cos(pi/4))/(sin x)`

Answer

`Rightarrow frac{d y}{d x}=frac{1}{sqrt{2}}(frac{2 x sin x-x^{2} cos x}{(sin x)^{2}})`

Explanation

We have:

`y=(x^{2} \cos \(pi / 4)) / \sin x`

Applying division rule of differentiation i.e

`\Rightarrow \frac{d}{d x}(\frac{t}{y})=\frac{y \cdot \frac{d t}{d x}-t \cdot \frac{d y}{d x}}{y^{2}}`

`Rightarrow y=\frac{x^2 \cos\(pi/4) }{\sin x } `
`=\frac{1}{\sqrt{2}} \frac{x^{2}}{\sin x}`

`\Rightarrow \frac{d y}{d x}=\frac{1}{\sqrt{2}}(\frac{\sin x \frac{d}{d x}(x^{2})-x^{2} \frac{d}{d x}(\sin x)}{(\sin x)^{2}})`

`\Rightarrow \frac{d y}{d x}=\frac{1}{\sqrt{2}}(\frac{2 x \sin x-x^{2} \cos x}{(\sin x)^{2}})`