Question

Derive:
Questão sobre derivada. Questões na imagem abaixo.

Answer 1

a)

f'(x) =5*0,7x^(5-1)-2*3*x^(2-1) +10

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b)

f'(x) =10*(x²-3x)^9  * (x²-3x)'

f'(x) =10*(x²-3x)^9  * (2x-3)

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c)

f'(x)=(x²)'*3^x + x²*(3^x)'

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u=3^x

ln u= ln 3^x

ln u=x* ln 3

u=e^(x* ln 3)

u'= (x* ln 3)' * e^(x* ln 3)

u'= ( ln 3) * e^(x* ln 3)

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f'(x)=2x**3^x + x²*( ln 3) * e^(x* ln 3)

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d)

f'(x)=[(5x+2)'*(3-x)-(5x+2)*(3-x)']/(3-x)²

f'(x)=[5*(3-x)-(5x+2)*(-1)]/(3-x)²

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e)

f'(x)=(3x^4-5x+2)'* e^(3x^4-5x+2)

f'(x)=(12x³-5)* e^(3x^4-5x+2)