Use Version 2 of the Chain Rule to calculate the

Joan Thompson

Joan Thompson

Answered question

2022-01-17

Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.
y=sin(4x3+3x+1)

Answer & Explanation

Debbie Moore

Debbie Moore

Beginner2022-01-18Added 43 answers

Step 1
We have to find the derivatives of the following function:
y=sin(4x3+3x+1)
We know the formula of derivatives,
dxndx=nxn1
daxndx=adxndx (where a is some constant)
dxdx=1
dadx=0
dsinxdx=cosx
dsin(f(x))dx=cos(f(x))df(x)dx (chain rule)
Step 2
Finding derivative of given function with respect to x by applying above formula, we get
dydx=dsin(4x3+3x+1)dx
=cos(4x3+3x+1)d(4x3+3x+1)dx
=cos(4x3+3x+1)(4dx3dx+3dxdx+d1dx)
=cos(4x3+3x+1)(4×3x31+3×1+0)
=cos(4x3+3x+1)(12x2+3)
=(12x2+3)cos(4x3+3x+1)
=3(4x2+1)cos(4x3+3x+1)
Hence, derivative of the function is
censoratojk

censoratojk

Beginner2022-01-19Added 46 answers

y=sin(4x3+3x+1)
dydx=ddxsin(4x3+3x+1)
=cos(4x3+3x+1)ddx(4x3+3x+1)
dydx=(12x2+3)cos(4x3+3x+1)
alenahelenash

alenahelenash

Expert2022-01-24Added 556 answers

Given function: y(x)=sin(4x3+3x+1)f(x)=sinx and g(x)=4x3+3x+1(fx)(x)=f(g(x))=f(4x3+3x+1)=sin(4x3+3x+1)ddx(f(g(x)))=f(g(x))g(x)=cos(4x3+3x+1)43x2+3=(12x2+3)cos(4x3+3x+1)Result:ddx(f(g(x)))=(12x2+3)cos(4x3+3x+1)

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