Question

if y=sin^2x,then d^2y/dx^2 is ?​

Answer 1

Answer:

y=sin^2x

or, dy/dx=2sinx cosx, [ dx^n/dx= nx^(n-1) ]

or, dy/dx=sin2x, [since,2sinx cosx=sin2x]

or, d^2y/dx^2=2cos2x

answer is d^2y/dx^2=2cos2x.

Answer 2

The second derivative of sin²x is 2cos2x.

Given:

y=sin^2x

To Find:

d^2y/dx^2

Solution:

We are required to find the second derivative of sin²x.

y=sin^2x

∵ d (xⁿ)/dx = nxⁿ⁻₁

∵ d (sin x)/dx = cos x

The above derivatives are used in the derivation of sin²x.

In the first derivative of sin²x,

dy/dx = d(sin²x)/dx    

          = 2sin x×cos x

          = sin2x

In the second derivative of sin²x,

d²y/dx² = d/dx(dy/dx)

             = d(sin2x)/dx

             = (cos2x)×2

             =2cos2x

Therefore, The second derivative of sin²x is 2cos2x.

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