Question

derivada formula general f(x)=
${2x}^{2} + 4x - 10$
ayuda porfavor


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Answer 1

Respuesta: f'(x)  = 4x + 4

Explicación paso a paso:

f'(x) = Lim (h→0) [f(x+h) - f(x)] / h

Tenemos que :

f(x+h) = 2(x+h)² + 4(x+h) - 10

f(x) = 2x² + 4x - 10

Entonces:

f'(x)  = Lim(h→0)[2(x+h)² + 4(x+h) - 10  -  (2x² + 4x - 10)] / h

f'(x) =Lim(h→0) [2(x² + 2xh + h²) + 4x + 4h - 10 - 2x² - 4x + 10] / h

f'(x) =Lim(h→0) [ 2x² + 4xh + 2h² + 4x + 4h - 10 - 2x² - 4x + 10] / h

f'(x) =Lim(h→0) [4xh + 2h² + 4h] / h

f'(x) = Lim(h→0){h.[4x + 2h + 4] / h}

f'(x) = Lim(h→0) [4x + 2h + 4]  

      =  4x + 4

f'(x)  = 4x + 4