What is the derivative of h(x)=sin⁡2xcos⁡2x

nemired9

nemired9

Answered

2021-12-26

What is the derivative of h(x)=sin2xcos2x

Answer & Explanation

Orlando Paz

Orlando Paz

Expert

2021-12-27Added 42 answers

Step 1
Product Rule of differentiation:
If f(x) and g(x) are any two differentiable functions, then
f(g)(x)=f(x)×g(x)+f(x)×g(x)
Chain rule of differentiation:
ddxf(g(x))=f(g(x))×ddxg(x)
=f(g(x))×g(x)×ddx(x)
=f(g(x))×g(x)
The given function is h(x)=sin2xcos2x
Step 2
Differentiate the given function using the product rule as follows.
h(x)=ddx(sin2xcos2x)
=sin2xddx(cos2x)+cos2xddx(sin2x)
(U sin g product rule)
=sin2x(sin2x)(2)+cos2x(cos2x)(2)
(U sin g chain rule)
=2sin22x+2cos22x
=2(1cos22x)+2cos22x
=2+4cos22x
Therefore, the derivative of the given function is
h(x)=2+4cos22x
peterpan7117i

peterpan7117i

Expert

2021-12-28Added 39 answers

Step 1
Given function:
sin(2x)cos(2x)
12(2sin(2x)cos(2x))
12sin(4x)
Differentiating given function w.r.t x as follows
ddx(12sin(4x))
=12ddx(sin(4x))
=12cos(4x)ddx(4x)
=12cos(4x)(4)
=2cos(4x)
karton

karton

Expert

2022-01-04Added 439 answers

Expalnation:
differentiate using the productchain rule
Giveny=f(x)g(x)dydx=f(x)g(x)+g(x)f(x)product rulef(x)=sin2xf(x)=2cos2xg(x)=cos2xg(x)=2sin2xddx(sin2xcos2x)=2sin22x+2cos22x=2(cos22xsin22x)=2cos4x

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