Verified answer

Hola

Función confusa...

y = x^2 sen^2(x^2)

Para

x = (π/2)^(1/2) -> x^2 = (π/2)

y = (π/2) * sen^2((π/2))

y = (π/2) * (1)^2

y = (π/2)

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Derivada de

y = x^2 sen^2(x^2)

Derivada de producto

y' = (x^2)' sen^2(x^2) + x^2 (sen^2(x^2))'

Derivada de x^2 ; sen^2

y' = (2 x) sen^2(x^2) + x^2 (2 sen(x^2) (sen(x^2))' )

Derivada de seno

y' = (2 x) sen^2(x^2) + x^2 (2 sen(x^2) cos(x^2) (x^2)' )

Derivada de x^2

y' = (2 x) sen^2(x^2) + x^2 (2 sen(x^2) cos(x^2) (2 x) )

Agrupamos

y' = 2 x sen^2(x^2) + 4 x^3 sen(x^2) cos(x^2)

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Para

x = (π/2)^(1/2) -> x^2 = (π/2)

y' = 2 (π/2)^(1/2) * sen((π/2)) + 4 ((π/2)^(3/2)) sen((π/2)) cos((π/2))

y' = 2 (π/2)^(1/2) * 1 + 4 ((π/2)^(3/2)) * 1 * 0

Pendiente de recta tangente (derivada)

y' = 2 (π/2)^(1/2)

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Recta tangente pasante por

x = (π/2)^(1/2) ; y = (π/2)

y - (π/2) = (2 (π/2)^(1/2)) (x - (π/2)^(1/2))

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Nos preguntan dónde corta el eje y esta recta

Para x = 0

yo - (π/2) = (2 (π/2)^(1/2)) (0 - (π/2)^(1/2))

yo - (π/2) = (-2) (π/2)^(1/2) * (π/2)^(1/2)

yo - (π/2) = (-2) (π/2)

yo = (π/2) + (-2) (π/2)

yo = (-π/2)

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