Question

derivative of sin2x cos^2x​

Answer 1

Answer:

to find the value of sin 2x into cos 2x , trigonometry Double angle formula used. for the derivation Kumar the value of sin2x and cos2x are used from trigonometry angle formulas,

sin 2x =2 sinx cosx------------(1)

And,

cos 2x = cos^2x - sin^2x

= 2cos^2 - 1----------(2)[sincesin^2

x + cos^2x = 1]

=1 -2sin^2x----------(3)

Now, to get the value of the sin

2x cos 2x, multiply question 1 with two 2 or 1

consider equation 1 and 2

sin2x = 2 sin x cos x and cos2x = 2x cos square x -1

multiply them to get,

sin^2 x cos square X = 2 sin x cos x (2 x square -1)

=4 sinx cos^3x - 2 sinx cos^2x - sin x)

Now, consider equation 1 and 3

sin 2x =2 sinx cosx

And,

cos2x =1-2sin^2x

multiply them to get

sin2x cos2x - 4sin^2x cosx

=2 sinx cosx - 4sin^2x cosx

=2cosx ( sin x-2 sin^3x)

so

sin2x cos2x = 2cosx ( 2sin x cos^2x- sinx)

Step-by-step explanation:

Derivative of sin2x cos2x

d/dx (sin2x cos2x) = 2cos(4x)

Proof:

sin 2x cos 2x

1/2 [ 2sin (2x) cos (2x)]

or 1/2 sin (4x)

Now, differentiate the given function w.f.t.x:

d /dx [1/2 sin (4x)]

= 1/2 [(d) dx (sin(4)]

=1/2[cos (4x)d (dx (4x))]

= 1/2 [cos (4x)(4)]

so,d/dx (sin2x cos2x) = 2cos (4x)

it may help you!!

bye good night! !!