Check the solution to "Find the derivatives of the functions y=x2cot⁡5x"

College
Calculus and Analysis
Differential Calculus
Derivatives

Kaycee Roche

Answered question

2021-10-15

Find the derivatives of the functions

y = x^{2} \cot 5 x

Answer & Explanation

pattererX

Skilled2021-10-16Added 95 answers

Given,
$y = x^{2} \cot 5 x$
Differentiating with respect to x, we get
$\frac{d y}{d x} = \frac{d (x^{2})}{d x} \cdot \cot 5 x + \frac{d (\cot 5 x)}{d x} \cdot x^{2} [∵ \frac{d (u \cdot v)}{d x} = \frac{d u}{d x} \cdot v + \frac{d v}{d x} \cdot u]$
$\Rightarrow \frac{d y}{d x} = 2 x \cdot \cot 5 x - \csc^{2} (5 x) \cdot \frac{d (5 x)}{d x} \cdot x^{2} [∵ \frac{d (x^{n})}{d x} = n x^{n - 1} \frac{d (\cot x)}{d x} = - \csc^{2} x]$
$\Rightarrow \frac{d y}{d x} = 2 x \cdot \cot 5 x - \csc^{2} (5 x) \cdot 5 \cdot x^{2}$
$\Rightarrow \frac{d y}{d x} = 2 x \cot 5 x - 5 x^{2} \csc^{2} (5 x)$

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