2/3 nhân y + 1/3 +( y+34 ) =5/6
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NV
Nguyễn Việt Lâm
Giáo viên
2 tháng 1 2024
Coi như tất cả các biểu thức cần tính đạo hàm đều xác định.
1.
\(y'=2sin\sqrt{4x+3}.\left(sin\sqrt{4x+3}\right)'=2sin\sqrt{4x+3}.cos\sqrt{4x+3}.\left(\sqrt{4x+3}\right)'\)
\(=sin\left(2\sqrt{4x+3}\right).\dfrac{4}{2\sqrt{4x+3}}=\dfrac{2sin\left(2\sqrt{4x+3}\right)}{\sqrt{4x+3}}\)
2.
\(y'=3x^3+\dfrac{17}{x\sqrt{x}}\)
3.
\(y'=\dfrac{1}{2\sqrt{\dfrac{sin4x}{cos\left(x^2+2\right)}}}.\left(\dfrac{sin4x}{cos\left(x^2+2\right)}\right)'\)
\(=\dfrac{1}{2\sqrt{\dfrac{sin4x}{cos\left(x^2+2\right)}}}.\dfrac{4cos4x.cos\left(x^2+2\right)+2x.sin4x.sin\left(x^2+2\right)}{cos^2\left(x^2+2\right)}\)
NV
Nguyễn Việt Lâm
Giáo viên
2 tháng 1 2024
4.
\(y'=-\dfrac{\left(\sqrt{sin^2\left(6-x\right)+4x}\right)'}{sin^2\left(6-x\right)+4x}=-\dfrac{\left[sin^2\left(6-x\right)+4x\right]'}{2\sqrt{\left[sin^2\left(6-x\right)+4x\right]^3}}\)
\(=-\dfrac{2sin\left(6-x\right).\left[sin\left(6-x\right)\right]'+4}{2\sqrt{\left[sin^2\left(6-x\right)+4x\right]^3}}=-\dfrac{-2sin\left(6-x\right).cos\left(6-x\right)+4}{2\sqrt{\left[sin^2\left(6-x\right)+4x\right]^3}}\)
\(=\dfrac{sin\left(12-2x\right)-4}{2\sqrt{\left[sin^2\left(6-x\right)+4x\right]^3}}\)
5.
\(y'=sin^2\left(\dfrac{2x-1}{4-x}\right)+2x.sin\left(\dfrac{2x-1}{4-x}\right).\left[sin\left(\dfrac{2x-1}{4-x}\right)\right]'\)
\(=sin^2\left(\dfrac{2x-1}{4-x}\right)+2x.sin\left(\dfrac{2x-1}{4-x}\right).cos\left(\dfrac{2x-1}{4-x}\right).\left(\dfrac{2x-1}{4-x}\right)'\)
\(=sin^2\left(\dfrac{2x-1}{4-x}\right)+x.sin\left(\dfrac{4x-2}{4-x}\right).\dfrac{7}{\left(4-x\right)^2}\)
TN
1
18 tháng 9 2021
\(\left(5-y\right)^6-2\left(5-y\right)^3+1\)
\(=\left[\left(5-y\right)^3-1\right]^2\)
\(=\left(125-75y+15y^2+y^3-1\right)^2\)
\(=\left(124-75y+15y^2+y^3\right)^2\)
MH
3 tháng 10 2021
1) \(2xy^3-6x^2+10xy\)
\(=2x.y^3-2x.3x+2x.5y\)
\(=2x\left(y^3-3x+5y\right)\)
\(=2x[y\left(y^2-5\right)-3x]\)
PT
1
5 tháng 10 2017
\(\frac{7}{4}-y\cdot\frac{5}{6}=\frac{1}{2}+\frac{1}{3}\)
\(\frac{7}{4}-y\cdot\frac{5}{6}=\frac{5}{6}\)
\(y\cdot\frac{5}{6}=\frac{7}{4}-\frac{5}{6}\)
\(y\cdot\frac{5}{6}=\frac{11}{12}\)
\(y=\frac{11}{12}:\frac{5}{6}\)
\(y=\frac{11}{10}\)
4 tháng 12 2023
1: \(x\left(x-1\right)+\left(1+x\right)^2\)
\(=x^2-x+x^2+2x+1\)
\(=2x^2+x+1\)
Đa thức này ko phân tích được nha bạn
2: \(\left(x+1\right)^2-3\left(x+1\right)\)
\(=\left(x+1\right)\cdot\left(x+1\right)-\left(x+1\right)\cdot3\)
\(=\left(x+1\right)\left(x+1-3\right)\)
\(=\left(x+1\right)\left(x-2\right)\)
3: \(2x\cdot\left(x-2\right)-\left(x-2\right)^2\)
\(=2x\left(x-2\right)-\left(x-2\right)\cdot\left(x-2\right)\)
\(=\left(x-2\right)\left(2x-x+2\right)\)
\(=\left(x-2\right)\left(x+2\right)\)
4: \(3x\left(x-1\right)^2-\left(1-x\right)^3\)
\(=3x\left(x-1\right)^2+\left(x-1\right)^3\)
\(=3x\left(x-1\right)^2+\left(x-1\right)^2\cdot\left(x-1\right)\)
\(=\left(x-1\right)^2\cdot\left(3x+x-1\right)\)
\(=\left(x-1\right)^2\cdot\left(4x-1\right)\)
5: \(3x\left(x+2\right)-5\left(x+2\right)^2\)
\(=\left(x+2\right)\cdot3x-\left(x+2\right)\cdot\left(5x+10\right)\)
\(=\left(x+2\right)\left(3x-5x-10\right)\)
\(=\left(-2x-10\right)\left(x+2\right)\)
\(=-2\left(x+5\right)\left(x+2\right)\)
6: \(4x\left(x-y\right)+3\left(y-x\right)^2\)
\(=4x\left(x-y\right)+3\left(x-y\right)^2\)
\(=\left(x-y\right)\cdot4x+\left(x-y\right)\left(3x-3y\right)\)
\(=\left(x-y\right)\cdot\left(4x+3x-3y\right)\)
\(=\left(x-y\right)\left(7x-3y\right)\)
\(\frac{2}{3}.y+\frac{1}{3}+\left(y+34\right)=\frac{5}{6}\)
\(=\frac{2}{3}.y+\frac{1}{3}+y+34=\frac{5}{6}\)
\(=y\left(\frac{2}{3}+1\right)+\left(\frac{1}{3}+34\right)=\frac{5}{6}\)
\(=\frac{5}{3}y+\frac{103}{3}=\frac{5}{6}\)
\(=\frac{5}{3}y=\frac{5}{6}-\frac{103}{3}=-\frac{67}{2}\)
\(y=-\frac{67}{2}:\frac{5}{3}=-\frac{201}{10}=-20,1\)