If y=a cos (sin 2 x)+b sin (sin 2 x), then y^ | vedclass

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

Question

(C) Given, $y=a \cos (\sin 2 x)+b \sin (\sin 2 x)$.On differentiating both sides with respect to $x$, we get:$y^{\prime} = -a \sin(\sin 2x) \cdot \cos

Vedclass · Accepted Answer

$-4(\cos ^2 2 x) y$

Vedclass · Answer

(C) Given, $y=a \cos (\sin 2 x)+b \sin (\sin 2 x)$.On differentiating both sides with respect to $x$, we get:$y^{\prime} = -a \sin(\sin 2x) \cdot \cos 2x \cdot 2 + b \cos(\sin 2x) \cdot \cos 2x \cdot 2$$y^{\prime} = 2 \cos 2x \{-a \sin(\sin 2x) + b \cos(\sin 2x)\}$.Again, differentiating with respect to $x$ using the product rule:$y^{\prime \prime} = -4 \sin 2x \{-a \sin(\sin 2x) + b \cos(\sin 2x)\} + 2 \cos 2x \{-a \cos(\sin 2x) \cdot \cos 2x \cdot 2 - b \sin(\sin 2x) \cdot \cos 2x \cdot 2\}$.Substituting $y^{\prime} = 2 \cos 2x \{-a \sin(\sin 2x) + b \cos(\sin 2x)\}$ into the first part:$y^{\prime \prime} = -4 \sin 2x \cdot \frac{y^{\prime}}{2 \cos 2x} - 4 \cos^2 2x \{a \cos(\sin 2x) + b \sin(\sin 2x)\}$.Since $y = a \cos(\sin 2x) + b \sin(\sin 2x)$, we have:$y^{\prime \prime} = -2 	an 2x \cdot y^{\prime} - 4 \cos^2 2x \cdot y$.Therefore, $y^{\prime \prime} + (2 	an 2x) y^{\prime} = -4 \cos^2 2x \cdot y$.

If $y=a \cos (\sin 2 x)+b \sin (\sin 2 x)$, then $y^{\prime \prime}+(2 \tan 2 x) y^{\prime}$ is equal to

Similar Questions

If $y = (\sin^{-1} x)^2$, then $(1 - x^2) \frac{d^2 y}{dx^2} - x \frac{dy}{dx} = $

If $y = {\left[ {x + \sqrt {{x^2} - 1} } \right]^{15}} + {\left[ {x - \sqrt {{x^2} - 1} } \right]^{15}}$,then $\left( {{x^2} - 1} \right)\frac{{{d^2}y}}{{d{x^2}}} + x\frac{{dy}}{{dx}}$ is equal to

If ${I_n} = \frac{d^n}{dx^n}(x^n \log x)$,then ${I_n} - n{I_{n - 1}} = $

Let $f(x)$ be a twice differentiable function such that $f''(x) = -f(x)$, $f'(x) = g(x)$, and $h(x) = \{f(x)\}^2 + \{g(x)\}^2$. If $h(5) = 11$, then $h(10)$ is equal to ...

If $y=a \cos 3 x+b e^{-x}$, then $y^{\prime \prime}(3 \sin 3 x-\cos 3 x)=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module