If y = sin x cdot sin 2x cdot sin 3x cdot ldo | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given,$y = \sin x \cdot \sin 2x \cdot \sin 3x \cdot \ldots \cdot \sin nx$.Taking the natural logarithm on both sides:$\ln y = \ln(\sin x) + \ln(\s

Vedclass · Accepted Answer

$y \cdot \sum_{k=1}^{n} k \cot kx$

Vedclass · Answer

(B) Given,$y = \sin x \cdot \sin 2x \cdot \sin 3x \cdot \ldots \cdot \sin nx$.Taking the natural logarithm on both sides:$\ln y = \ln(\sin x) + \ln(\sin 2x) + \ln(\sin 3x) + \ldots + \ln(\sin nx)$Differentiating both sides with respect to $x$ using the chain rule:$\frac{1}{y} \cdot y^{\prime} = \frac{d}{dx}(\ln \sin x) + \frac{d}{dx}(\ln \sin 2x) + \ldots + \frac{d}{dx}(\ln \sin nx)$$\frac{y^{\prime}}{y} = \frac{\cos x}{\sin x} + 2 \cdot \frac{\cos 2x}{\sin 2x} + 3 \cdot \frac{\cos 3x}{\sin 3x} + \ldots + n \cdot \frac{\cos nx}{\sin nx}$$\frac{y^{\prime}}{y} = \sum_{k=1}^{n} k \cot kx$Therefore,$y^{\prime} = y \cdot \sum_{k=1}^{n} k \cot kx$.

If $y = \sin x \cdot \sin 2x \cdot \sin 3x \cdot \ldots \cdot \sin nx$,then $y^{\prime}$ is

Similar Questions

Differentiate $x^{\sin x}, x > 0$ with respect to $x$.

If $f(\theta) = \cos \theta_1 \cdot \cos \theta_2 \cdot \cos \theta_3 \cdots \cos \theta_n$,then $\tan \theta_1 + \tan \theta_2 + \tan \theta_3 + \cdots + \tan \theta_n =$

If ${x^m}{y^n} = 2{(x + y)^{m + n}},$ the value of $\frac{dy}{dx}$ is

If $y=(\log x)^{1/x} + x^{\log x}$,find $\frac{dy}{dx}$ at $x=e$.

Find the derivative: $\frac{d}{dx}(x^{\log_e x})$

Vedclass Test Series

Exam Paper Generator

Online Exam Module