Question

Determine a derivada de f(x) = 5x2 no ponto x0 = 5.

Answer 1

f'(x) = 2.5.x = 10.x

f'(5) = 10.5 = 50

Answer 2

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Derivada no ponto

$\sf f(x)=5x^2\\\sf f(5)=5\cdot5^2=125\\\displaystyle\sf f'(5)=\lim_{x \to 5}\dfrac{5x^2-125}{x-5}=\lim_{x \to 5}\dfrac{5\cdot(x^2-25)}{x-5}\\\displaystyle\sf f'(5)=\lim_{x \to 5}\dfrac{5\cdot\diagup\!\!\!\!\!(x-\diagup\!\!\!\!\!5)(x+5)}{\diagup\!\!\!\!\!x-\diagup\!\!\!\!\!5}\\\displaystyle\sf f'(5)=5\lim_{x \to 5}(x+5)=5\cdot(5+5)\\\sf f'(5)=5\cdot10\\\huge\boxed{\boxed{\boxed{\boxed{\sf f'(5)=50\checkmark}}}}$