a função derivada de f(x) =(6x+1)(x²+2)
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f(x) =(6x+1)(x²+2)
f(x)' =(6x+1)'(x²+2) + (6x+1)(x²+2)'
f(x)' = 6(x²+2) + (6x+1)(2x)
f(x)' = 6x² + 12 + 12x² + 2x
f(x)' = 18x² + 2x + 12
Respondido por
1
Boa tarde!
Solução!
Temos aqui o produto de duas funções,logo vamos fazer a derivada do produto.
![f(x)=(6x+1)( x^{2} +2)\\\\\\
u=6x+1~~~~~v=( x^{2} +2)\\\\\\
u'=6~~~~~~~v'=2x\\\\\\\
f'(x)=u.v'+u'v\\\\\\\
f'(x)=(6x+1).(2x)+(6).( x^{2} +2)\\\\\\
f'(x)=(12 x^{2} +2x)+(6 x^{2} +12)\\\\\\
f'(x)=(12 x^{2}+6 x^{2}+2x +12)\\\\\\
f'(x)=(18 x^{2} +2x+12)\\\\\\](https://tex.z-dn.net/?f=f%28x%29%3D%286x%2B1%29%28+x%5E%7B2%7D+%2B2%29%5C%5C%5C%5C%5C%5C%0Au%3D6x%2B1%7E%7E%7E%7E%7Ev%3D%28+x%5E%7B2%7D+%2B2%29%5C%5C%5C%5C%5C%5C%0Au%27%3D6%7E%7E%7E%7E%7E%7E%7Ev%27%3D2x%5C%5C%5C%5C%5C%5C%5C%0Af%27%28x%29%3Du.v%27%2Bu%27v%5C%5C%5C%5C%5C%5C%5C%0Af%27%28x%29%3D%286x%2B1%29.%282x%29%2B%286%29.%28+x%5E%7B2%7D+%2B2%29%5C%5C%5C%5C%5C%5C%0Af%27%28x%29%3D%2812+x%5E%7B2%7D+%2B2x%29%2B%286+x%5E%7B2%7D+%2B12%29%5C%5C%5C%5C%5C%5C%0Af%27%28x%29%3D%2812+x%5E%7B2%7D%2B6+x%5E%7B2%7D%2B2x+%2B12%29%5C%5C%5C%5C%5C%5C%0Af%27%28x%29%3D%2818+x%5E%7B2%7D+%2B2x%2B12%29%5C%5C%5C%5C%5C%5C "f(x)=(6x+1)( x^{2} +2)\\\\\\
u=6x+1~~~~~v=( x^{2} +2)\\\\\\
u'=6~~~~~~~v'=2x\\\\\\\
f'(x)=u.v'+u'v\\\\\\\
f'(x)=(6x+1).(2x)+(6).( x^{2} +2)\\\\\\
f'(x)=(12 x^{2} +2x)+(6 x^{2} +12)\\\\\\
f'(x)=(12 x^{2}+6 x^{2}+2x +12)\\\\\\
f'(x)=(18 x^{2} +2x+12)\\\\\\")
Boa tarde!
Bons estudos!
Solução!
Temos aqui o produto de duas funções,logo vamos fazer a derivada do produto.
Boa tarde!
Bons estudos!
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