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בעיות פופולריות

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בעיות חשבון אינפיטסימלי פופולריות

(\partial)/(\partial x)(7sqrt(x^2+y^2))	∂ ∂ `x` (7√`x`²+`y`²)
tangent f(x)=x^4-5x^2+2,\at x=2	`tangent` `f`(`x`)=`x`⁴−5`x`²+2,at `x`=2
derivative of 5(e^xcos(x-e^xsin(x)))	`ddx` (5(`e`^xcos(`x`)−`e`^xsin(`x`)))
integral of xsqrt(6-x)	∫ `x`√6−`xdx`
limit as x approaches 3 of (x-1)/(x^2-1)	lim _{x→ 3}(`x`−1`x`²−1 )
inverselaplace e^{-2s} 1/(s-9)	`inverselaplace` `e`^−2s1`s`−9
integral of 1/(sqrt(1+\sqrt{x))}	∫ 1√1+√`x` `dx`
slope (0,-6),(3,-5)	`slope` (0,−6),(3,−5)
derivative y= 6/(\sqrt[4]{x)}	`derivative` `y`=6⁴√`x`
limit as t approaches 0 of (sin(3t)+4t)/(tsec(t))	lim _{t→ 0}(sin(3`t`)+4`tt`sec(`t`) )
(\partial)/(\partial y)(5xln(xy))	∂ ∂ `y` (5`x`ln(`xy`))
(\partial)/(\partial x)(y^2cos(x))	∂ ∂ `x` (`y`²cos(`x`))
(\partial)/(\partial x)(sin(9x+yz))	∂ ∂ `x` (sin(9`x`+`yz`))
derivative of (x^3-2x+4/(x^3))	`ddx` (`x`³−2`x`+4`x`³ )
integral of x(5x-3)^2	∫ `x`(5`x`−3)²`dx`
integral of e^{3x}+1/x	∫ `e`^3x+1`x` `dx`
derivative of x(dy/(dx))	`ddx` (`xdydx` )
y^'+3y=2e^{-3t}	`y`^′+3`y`=2`e`^−3t
derivative f(x)=((sqrt(x)-2))/((2x^2+3))	`derivative` `f`(`x`)=(√`x`−2)(2`x`²+3)
integral from 2 to 3 of 1/(x^2-4x)	∫ ₂³1`x`²−4`x` `dx`
derivative 3x^4-5x+2\sqrt[3]{x}	`derivative` 3`x`⁴−5`x`+2³√`x`
derivative of ln(1-6x)	`ddx` (ln(1−6`x`))
tangent-x^2+3x+4,\at x=1	`tangent` −`x`²+3`x`+4,at `x`=1
(dy}{dx}=\frac{-e^x)/8	`dydx` =−`e`^x8
(\partial)/(\partial y)(xye^z)	∂ ∂ `y` (`xye`^z)
derivative cos(7x)	`derivative` cos(7`x`)
limit as x approaches-1-of {2x^2-5x}	lim _{x→ −1−}({2`x`²−5`x`})
derivative of 3sec^2(pix-1)	`ddx` (3sec²(π`x`−1))
tangent f(x)=(x^2)/(x+1),\at x=2	`tangent` `f`(`x`)=`x`²`x`+1 ,at `x`=2
integral of 20(e^{3/4 x}-e^{2x})	∫ 20(`e`^34 x−`e`^2x)`dx`
integral from 4 to infinity of 7e^{-y/2}	∫ ₄^∞7`e`^−y2`dy`
(\partial)/(\partial y)(xye^{x+y})	∂ ∂ `y` (`xye`^x+y)
integral of (sin(2x)-sin(3x))^2	∫ (sin(2`x`)−sin(3`x`))²`dx`
tangent f(x)= 5/x ,(3, 5/3)	`tangent` `f`(`x`)=5`x` ,(3,53 )
(\partial)/(\partial t)(e^{-2x}cos(9pit))	∂ ∂ `t` (`e`^−2xcos(9π`t`))
taylor 1/2 arctan(2x)	`taylor` 12 arctan(2`x`)
sum from n=1 to infinity of 3e^{-4n}	∑ _n=1^∞3`e`⁻⁴ⁿ
tangent f(x)= 1/(x^2+4),(1, 1/5)	`tangent` `f`(`x`)=1`x`²+4 ,(1,15 )
integral of 3e^x-3xe^{x^2}	∫ 3`e`^x−3`xe`^x²`dx`
integral of ,^2x	∫ ,²`xdx`
derivative of kx+d	`ddx` (`kx`+`d`)
derivative of 2(x-2^2+1)	`ddx` (2(`x`−2)²+1)
integral of 1/(2x^3-3x^2)	∫ 12`x`³−3`x`² `dx`
derivative x^2(3-x)	`derivative` `x`²(3−`x`)
derivative cy^{-6}	`derivative` `cy`⁻⁶
limit as x approaches 1 of x^3-2x^2+x-3	lim _{x→ 1}(`x`³−2`x`²+`x`−3)
derivative x^6	`derivative` `x`⁶
derivative of (90/x)	`ddx` (90`x` )
limit as x approaches infinity of x^2+1	lim _{x→ ∞}(`x`²+1)
derivative of 1/3 pix^2y	`ddx` (13 π`x`²`y`)
integral of tan^4(7x)	∫ tan⁴(7`x`)`dx`
(\partial)/(\partial x)(cos(x)sin(x)-xy)	∂ ∂ `x` (cos(`x`)sin(`x`)−`xy`)
(\partial)/(\partial x)(4)	∂ ∂ `x` (4)
derivative ax+b	`derivative` `ax`+`b`
tangent ((3x))/((1+x^2))	`tangent` (3`x`)(1+`x`²)
integral of tan(5v)sec(5v)	∫ tan(5`v`)sec(5`v`)`dv`
(dy)/(dt)=20-y/(230+t)	`dydt` =20−`y`230+`t`
inverselaplace 1/((x+3)^2)	`inverselaplace` 1(`x`+3)²
integral of tanh(x)	∫ tanh(`x`)`dx`
(\partial)/(\partial z)(xyz^2)	∂ ∂ `z` (`xyz`²)
derivative of sin(3x+cos(3x))	`ddx` (sin(3`x`)+cos(3`x`))
integral of 7arccos(x)	∫ 7arccos(`x`)`dx`
integral of 1/(sqrt(x^2+b^2))	∫ 1√`x`²+`b`² `dx`
integral of sqrt(e^{2x)+x}*(e^{2x}+1/2)	∫ √`e`^2x+`x`· (`e`^2x+12 )`dx`
derivative f(x)=x^x(ln(x)+1)	`derivative` `f`(`x`)=`x`^x(ln(`x`)+1)
derivative f(x)=xe^{4x}	`derivative` `f`(`x`)=`xe`^4x
(\partial)/(\partial y)(sin(x^2-y^2))	∂ ∂ `y` (sin(`x`²−`y`²))
derivative cos(e^x)	`derivative` cos(`e`^x)
integral from 1 to infinity of 3^{-x}	∫ ₁^∞3^−x`dx`
integral from 0 to 3 of sqrt(5)	∫ ₀³√5`dx`
integral of-ln(1-x)	∫ −ln(1−`x`)`dx`
tangent sqrt(x)+sqrt(y)=sqrt(2)	`tangent` √`x`+√`y`=√2
integral of cos^3(x/(18))	∫ cos³(`x`18 )`dx`
integral of (sqrt(5x+1))	∫ (√5`x`+1)`dx`
tangent y=(5x)/(x+2),(3,3)	`tangent` `y`=5`xx`+2 ,(3,3)
(\partial)/(\partial x)(1(x-y)e^{y+2x^2})	∂ ∂ `x` (1(`x`−`y`)`e`^y+2x²)
y+y^{''}=0	`y`+`y`^{′ ′}=0
limit as x approaches 0+of x/(x+\|x\|)	lim _{x→ 0+}(`xx`+\|`x`\| )
(\partial)/(\partial x)(z^3-3xyz)	∂ ∂ `x` (`z`³−3`xyz`)
(\partial)/(\partial x)(e^{9xe^y})	∂ ∂ `x` (`e`^{9xe^y})
(\partial)/(\partial x)(sin^2(3x))	∂ ∂ `x` (sin²(3`x`))
integral of csc^9(x)	∫ csc⁹(`x`)`dx`
limit as x approaches 0 of x^2-3x+3	lim _{x→ 0}(`x`²−3`x`+3)
derivative of (2x/(sqrt(x)))	`ddx` (2`x`√`x` )
limit as x approaches 0+of 3/x	lim _{x→ 0+}(3`x` )
integral of x^{27}e^{x^{28}}	∫ `x`²⁷`e`^x²⁸`dx`
integral of cos^4(7x+8)	∫ cos⁴(7`x`+8)`dx`
integral of ln(10x)	∫ ln(10`x`)`dx`
y^'-4/x y=(y^3)/(x^4)	`y`^′−4`x` `y`=`y`³`x`⁴
integral of 5xe^{5x}	∫ 5`xe`^5x`dx`
integral of 1/(x^2-14x+68)	∫ 1`x`²−14`x`+68 `dx`
(dy)/(dx)+(y/x)=7x^3y^2	`dydx` +(`yx` )=7`x`³`y`²
(\partial)/(\partial x)(25x^{3/4}y^{1/4})	∂ ∂ `x` (25`x`³⁴`y`¹⁴)
integral of-csc^2(x)	∫ −csc²(`x`)`dx`
(dy)/(dt)=y	`dydt` =`y`
derivative y=sqrt(2x-1)	`derivative` `y`=√2`x`−1
tangent 7+2e^x-4x^4x-y=9	`tangent` 7+2`e`^x−4`x`⁴`x`−`y`=9
(\partial)/(\partial x)(x^{2x})	∂ ∂ `x` (`x`^2x)
limit as t approaches 1 of (t^3-1)/(t-1)	lim _{t→ 1}(`t`³−1`t`−1 )
limit as x approaches+0-of 6/(5x^{1/3)}	lim _{x→ +0−}(65`x`¹³ )

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