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Câu 8 trang 192 SGK Đại số và Giải tích 11 Nâng cao

Tìm đạo hàm của mỗi hàm số sau trên R.
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Tìm đạo hàm của mỗi hàm số sau trên R.

LG a

\(y = a{x^2}\) (a là hằng số)

Lời giải chi tiết:

Đặt  \(f(x)=y = a{x^2}\) Với \(x_0\in\mathbb R\) ta có: \(\eqalign{  & f'\left( {{x_0}} \right) = \mathop {\lim }\limits_{\Delta x \to 0} {{f\left( {{x_0} + \Delta x} \right) - f\left( {{x_0}} \right)} \over {\Delta x}}  \cr  &  = \mathop {\lim }\limits_{\Delta x \to 0} {{a{{\left( {{x_0} + \Delta x} \right)}^2} - ax_0^2} \over {\Delta x}}  \cr  &  = \mathop {\lim }\limits_{\Delta x \to 0} a\left( {2{x_0} + \Delta x} \right) = 2a{x_0} \cr} \)

Cách trình bày khác:

LG b

\(y = {x^3} + 2\)

Lời giải chi tiết:

Đặt \(f(x)=y = {x^3} + 2\) Với \(x_0\in\mathbb R\) ta có: \(\eqalign{  & f'\left( {{x_0}} \right) = \mathop {\lim }\limits_{\Delta x \to 0} {{f\left( {{x_0} + \Delta x} \right) - f\left( {{x_0}} \right)} \over {\Delta x}}  \cr  &  = \mathop {\lim }\limits_{\Delta x \to 0} {{{{\left( {{x_0} + \Delta x} \right)}^3} + 2 - x_0^3 - 2} \over {\Delta x}}  \cr  &  = \mathop {\lim }\limits_{\Delta x \to 0} \left[ {{{\left( {{x_0} + \Delta x} \right)}^2} + \left( {{x_0} + \Delta x} \right){x_0} + x_0^2} \right] \cr &= 3x_0^2 \cr} \)

Cách trình bày khác:

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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