If y-e4x sin 2x- then dy dx-

The correct option is A Here u=e^4x v=sin^2x, Differentiating both sides w.r.t. 'x' dy dx=d dx[e^4x sin2x] =e^4xd dx[sin 2x]+sin 2xd dx[e^4x](Using product r ...

You visited us 2 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Chain Rule of Differentiation

If y=e4x sin ...

Question

If $y = e^{4 x} s i n 2 x$ , then $\frac{d y}{d x}$ =?

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

none of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C

Here $u = e^{4 x} v = s i n^{2 x}$ , Differentiating both sides w.r.t. 'x'
$\frac{d y}{d x} = \frac{d}{d x} [e^{4 x} s i n 2 x]$
= $e^{4 x} \frac{d}{d x} [s i n 2 x] + s i n 2 x \frac{d}{d x} [e^{4 x}]$ (Using product rule)
= $2 e^{4 x} c o s 2 x + s i n 2 x 4 e^{4 x} = 2 e^{4 x} [c o s 2 x + 2 s i n 2 x]$

Suggest Corrections

Similar questions

If $y = c o s^{2} x, t h e n \frac{d y}{d x} = ?$

Q. If

\sin y = x \cos (a + y), then \frac{d y}{d x}

is equal to
(a)

\frac{\cos^{2} (a + y)}{\cos a}

(b)

\frac{\cos a}{\cos^{2} (a + y)}

(c)

\frac{\sin^{2} y}{\cos a}

(d) none of these

Q. If

y = \tan^{- 1} (\frac{\sin x + \cos x}{\cos x - \sin x}), then \frac{d y}{d x}

is equal to
(a)

\frac{1}{2}

(b) 0
(c) 1
(d) none of these

Q. If sin (π cos x) = cos (π sin x), then sin 2 x =

(a)

\pm \frac{3}{4}

(b)

\pm \frac{4}{3}

(c)

\pm \frac{1}{3}

(d) none of these

Q. If

y = \sqrt{\frac{1 - sin 2 x}{1 + sin 2 x}}

. Prove that

\frac{d y}{d x} + {sec}^{2} (\frac{π}{4} - x) = 0

Join BYJU'S Learning Program

If y=e4x sin2x, then dydx=?

The correct option is C Here u=e4x v=sin2x, Differentiating both sides w.r.t. 'x' dydx=ddx[e4x sin2x] =e4xddx[sin 2x]+sin 2xddx[e4x](Using product rule) =2e4xcos2x+sin2x 4e4x=2e4x[cos2x+2sin2x]

If $y = e^{4 x} s i n 2 x$ , then $\frac{d y}{d x}$ =?