Rút gọn tổng: \(S=C\overset{1}{2019}+2^2C\overset{2}{2019}+...+2018^2C\overset{2018}{2019}+2019^2C\overset{2019}{2019}\) bằng:

A. \(2019.2020.2^{2019}\)

B. \(2019.2^{2017}\)

C. \(2^{2019}\)

D. \(2019.505.2^{2019}\)

Rút gọn biểu thức \(S\left(x\right)=\dfrac{1}{x^2}+\dfrac{2}{x^3}+\dfrac{3}{x^4}+...+\dfrac{n}{x^{n+1}}\) bằng:

A. \(S=\dfrac{x^{n+1}-\left(n+1\right)x+n}{x^{n+1}\left(x-1\right)^2}\)

B. \(S=\dfrac{x^{n+1}-\left(n+1\right)x+n}{x^{2n}\left(x-1\right)^2}\)

C. \(S=\dfrac{x^n-\left(n+1\right)x+n}{x^n\left(x-1\right)^2}\)

D. \(S=\dfrac{x^{n+1}-\left(n+1\right)x+n}{x^n\left(x-1\right)^2}\)

Cho hàm số \(y=\dfrac{1}{\left(x-1\right)\left(x+3\right)}\). Hỏi đạo hàm cấp 2019 của hàm số bằng biểu thức nào sau đây?

A. \(\dfrac{2019!}{4}\left(\dfrac{1}{\left(x+3\right)^{2020}}+\dfrac{1}{\left(x-1\right)^{2020}}\right)\)

B. \(\dfrac{2019!}{4}\left(\dfrac{1}{\left(x+3\right)^{2020}}-\dfrac{1}{\left(x-1\right)^{2020}}\right)\)

C. \(-\dfrac{2019!}{4}\left(\dfrac{1}{\left(x+3\right)^{2020}}+\dfrac{1}{\left(x-1\right)^{2020}}\right)\)

D. \(-\dfrac{2019!}{4}\left(\dfrac{1}{\left(x+3\right)^{2020}}-\dfrac{1}{\left(x-1\right)^{2020}}\right)\)

Cho hàm số \(y=cos2x\). Tính đạo hàm cấp 2019 của hàm số:

A. \(y^{\left(2019\right)}=2^{2020}.cos2x\)

B. \(y^{\left(2019\right)}=-2^{2019}.cos2x\)

C. \(y^{\left(2019\right)}=-2^{2019}.sin2x\)

D. \(y^{\left(2019\right)}=2^{2019}.sin2x\)

Cho hàm số \(y=cos2x\). Tính đạo hàm cấp 2019 của hàm số:

A. \(y^{\left(2019\right)}=2^{2020}.cos2x\)

B. \(y^{\left(2019\right)}=-2^{2019}.cos2x\)

C. \(y^{\left(2019\right)}=-2^{2019}.sin2x\)

D. \(y^{\left(2019\right)}=2^{2019}.sin2x\)

Cho hàm số \(y=\dfrac{1}{2x^2+x-1}\). Hỏi đạo hàm cấp 2019 của hàm số bằng biểu thức nào sau đây?

A. \(\dfrac{2019!}{3}\left(\dfrac{1}{\left(x+1\right)^{2020}}-\dfrac{2^{2019}}{\left(2x-1\right)^{2020}}\right)\)

B. \(\dfrac{2019!}{3}\left(\dfrac{1}{\left(x+1\right)^{2020}}-\dfrac{2^{2020}}{\left(2x-1\right)^{2020}}\right)\)

C. \(\dfrac{2019!}{3}\left(\dfrac{1}{\left(x+1\right)^{2020}}-\dfrac{2}{\left(2x-1\right)^{2020}}\right)\)

D. \(\dfrac{2019!}{3}\left(\dfrac{1}{\left(x+1\right)^{2020}}+\dfrac{2}{\left(2x-1\right)^{2020}}\right)\)