savannaellis
Answered

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What is the derivative of (x + 1) sin x?

Sagot :

[tex]\boxed{\sf \dfrac{d}{dx}x^n=nx^{n-1}}[/tex]

[tex]\boxed{\sf \dfrac{d}{dx}sinx=cosx}[/tex]

Now

[tex]\\ \sf\longmapsto \dfrac{d}{dx}(x+1)sinx[/tex]

[tex]\\ \sf\longmapsto 1+cosx[/tex]

Anonimity

sin x + x · cos x + cos x

Step-by-step explanation:

  • (x + 1) = u → u' = 1
  • sin x = v → v' = cos x

f(x) = u · v → f'(x) = u' · v + u · v'

f(x) = (x + 1) sin x

f'(x) = 1 · sin x + (x + 1) · cos x

f'(x) = sin x + x · cos x + cos x

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