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Popular Calculus Problems

derivative of (x^{1-a}/(1-a))	\frac{d}{dx}(\frac{x^{1-a}}{1-a})
(\partial)/(\partial x)(({f}(x))^')	\frac{\partial\:}{\partial\:x}(({f}(x))^{\prime\:})
xy^{''}+y^'=x	xy^{\prime\:\prime\:}+y^{\prime\:}=x
derivative of (3x+4)/(7x-5)	derivative\:\frac{3x+4}{7x-5}
ay^'+by=0	ay^{\prime\:}+by=0
4tx(dx)/(dt)=x^2+1	4tx\frac{dx}{dt}=x^{2}+1
(\partial)/(\partial z)(cos(kz-wt))	\frac{\partial\:}{\partial\:z}(\cos(kz-wt))
inverse oflaplace 1/(2s^2+s+1)	inverselaplace\:\frac{1}{2s^{2}+s+1}
limit as x approaches 1 of (3x-4)^2	\lim\:_{x\to\:1}((3x-4)^{2})
derivative of f(x)=5-x^2	derivative\:f(x)=5-x^{2}
integral from 0 to 2 of 2x^4e^{-x}	\int\:_{0}^{2}2x^{4}e^{-x}dx
area y= 1/(14x^2),y=x,y= x/(10)	area\:y=\frac{1}{14x^{2}},y=x,y=\frac{x}{10}
d/(d{y)}(sqrt({x)+{y}{z}})	\frac{d}{d{y}}(\sqrt{{x}+{y}{z}})
x*y^'=sqrt(1-y^2)	x\cdot\:y^{\prime\:}=\sqrt{1-y^{2}}
(\partial)/(\partial y)(arctan(xsqrt(y)))	\frac{\partial\:}{\partial\:y}(\arctan(x\sqrt{y}))
derivative of (ax+by(x)/(cx+dy))	\frac{d}{dx}(\frac{ax+by(x)}{cx+dy})
derivative of (e^x-1/(e^x+1))	\frac{d}{dx}(\frac{e^{x}-1}{e^{x}+1})
derivative of 1/((x^4+1^3))	\frac{d}{dx}(\frac{1}{(x^{4}+1)^{3}})
tangent of 4.9x^{1.9},\at x=1.4	tangent\:4.9x^{1.9},\at\:x=1.4
derivative of x^aln(x)	\frac{d}{dx}(x^{a}\ln(x))
f(x)=5xe^x	f(x)=5xe^{x}
integral of (x^3-4x)	\int\:(x^{3}-4x)dx
(\partial)/(\partial u(v))((e^v)/(u(v)+v^4))	\frac{\partial\:}{\partial\:u(v)}(\frac{e^{v}}{u(v)+v^{4}})
integral of (sqrt(x))(x^2-3x-5)	\int\:(\sqrt{x})(x^{2}-3x-5)dx
integral of csc^4(x)cot^6(x)	\int\:\csc^{4}(x)\cot^{6}(x)dx
integral of sin(x)ln(x)	\int\:\sin(x)\ln(x)dx
derivative of f(x)= 9/(sqrt(t))	derivative\:f(x)=\frac{9}{\sqrt{t}}
implicit (dy)/(dx),25x^2-10xy+4y^2=100	implicit\:\frac{dy}{dx},25x^{2}-10xy+4y^{2}=100
integral of ((x^3))/(sqrt(9-x^2))	\int\:\frac{(x^{3})}{\sqrt{9-x^{2}}}dx
(d^2)/(dx^2)(sqrt(x)^{e^x})	\frac{d^{2}}{dx^{2}}(\sqrt{x}^{e^{x}})
derivative of h(x)=((3x-5))/(1-x^2)	derivative\:h(x)=\frac{(3x-5)}{1-x^{2}}
derivative of sqrt(3x^2)	\frac{d}{dx}(\sqrt{3x^{2}})
derivative of 2x^3+(5x+1/(3x-5)-2/(x^3))	\frac{d}{dx}(2x^{3}+\frac{5x+1}{3x-5}-\frac{2}{x^{3}})
y^'+y=8xe^x	y^{\prime\:}+y=8xe^{x}
derivative of 1/12 (x+2^3+(x+2)^{-1})	\frac{d}{dx}(\frac{1}{12}(x+2)^{3}+(x+2)^{-1})
limit as x approaches 0 of (7^x-9^x)/x	\lim\:_{x\to\:0}(\frac{7^{x}-9^{x}}{x})
derivative of g(t)=4t^{-1/8}	derivative\:g(t)=4t^{-\frac{1}{8}}
integral of 6/(3+x^2)	\int\:\frac{6}{3+x^{2}}dx
integral from (-2) to 8 of (\|x-2\|-3)	\int\:_{(-2)}^{8}(\left\|x-2\right\|-3)dx
integral from 0 to x^3 of ye^{(-y)/x}	\int\:_{0}^{x^{3}}ye^{\frac{-y}{x}}dy
integral from 0 to 13/6 of pi(13/6-x)^2	\int\:_{0}^{\frac{13}{6}}π(\frac{13}{6}-x)^{2}dx
(\partial)/(\partial x)(sin(pi(x-6y)))	\frac{\partial\:}{\partial\:x}(\sin(π(x-6y)))
integral of pi(4x)^2	\int\:π(4x)^{2}dx
integral of (x^2)/(sqrt(9+x^2))	\int\:\frac{x^{2}}{\sqrt{9+x^{2}}}dx
derivative of (x^2-4^{1/3})	\frac{d}{dx}((x^{2}-4)^{\frac{1}{3}})
area x=-2,x=1,y=2x^2+4,y=0	area\:x=-2,x=1,y=2x^{2}+4,y=0
integral of x^3cos(nx)	\int\:x^{3}\cos(nx)dx
derivative of f(x)=sqrt(r)+\sqrt[9]{r}	derivative\:f(x)=\sqrt{r}+\sqrt[9]{r}
limit as x approaches-7 of x/(x-2)	\lim\:_{x\to\:-7}(\frac{x}{x-2})
slope of e^x+1	slope\:e^{x}+1
x^2y+y^'=-7x^2	x^{2}y+y^{\prime\:}=-7x^{2}
limit as x approaches infinity of 3x+6	\lim\:_{x\to\:\infty\:}(3x+6)
taylor ln(1+6x)	taylor\:\ln(1+6x)
limit as x approaches 2 of x/(ln(x-1))	\lim\:_{x\to\:2}(\frac{x}{\ln(x-1)})
limit as x approaches-2 of sqrt(x^3+1)	\lim\:_{x\to\:-2}(\sqrt{x^{3}+1})
integral of (x^2+4x-4)/(sqrt(x))	\int\:\frac{x^{2}+4x-4}{\sqrt{x}}dx
derivative of f(x)=6x^3-7x	derivative\:f(x)=6x^{3}-7x
derivative of \sqrt[3]{(2+3x/(2-3x)})	\frac{d}{dx}(\sqrt[3]{\frac{2+3x}{2-3x}})
inverse oflaplace ((e^{-3s}))/(s^2)	inverselaplace\:\frac{(e^{-3s})}{s^{2}}
(\partial)/(\partial y)(3x+x^2y)	\frac{\partial\:}{\partial\:y}(3x+x^{2}y)
limit as x approaches 1 of (ax^2-bx)^2	\lim\:_{x\to\:1}((ax^{2}-bx)^{2})
derivative of 2ce^{2x}	\frac{d}{dx}(2ce^{2x})
(dy)/(dx)=((2x(y-2)))/(x^2+1),y(0)=4	\frac{dy}{dx}=\frac{(2x(y-2))}{x^{2}+1},y(0)=4
limit as t approaches 0 of e^{-t}	\lim\:_{t\to\:0}(e^{-t})
derivative of y= 1/2 (e^x+e^{-x})	derivative\:y=\frac{1}{2}(e^{x}+e^{-x})
integral of 2x(x^2-7)^{99}	\int\:2x(x^{2}-7)^{99}dx
(\partial)/(\partial y)(e^{xyz^8}yz^8)	\frac{\partial\:}{\partial\:y}(e^{xyz^{8}}yz^{8})
limit as x approaches 0 of (sin(x))^{5x}	\lim\:_{x\to\:0}((\sin(x))^{5x})
limit as x approaches 4 of 2/(sqrt(x-4))	\lim\:_{x\to\:4}(\frac{2}{\sqrt{x-4}})
integral of sec^2(4x)(3-tan(4x))^3	\int\:\sec^{2}(4x)(3-\tan(4x))^{3}dx
integral from-infinity to 4 of xe^{x/2}	\int\:_{-\infty\:}^{4}xe^{\frac{x}{2}}dx
y^'=-y-2x	y^{\prime\:}=-y-2x
integral of x(1-3x^2)^4	\int\:x(1-3x^{2})^{4}dx
derivative of ln(x)*x	derivative\:\ln(x)\cdot\:x
(\partial)/(\partial u)(4sin(u)cos(v))	\frac{\partial\:}{\partial\:u}(4\sin(u)\cos(v))
derivative of \sqrt[5]{x^4}-4/x	\frac{d}{dx}(\sqrt[5]{x^{4}}-\frac{4}{x})
limit as x approaches 0+of tan(2x)	\lim\:_{x\to\:0+}(\tan(2x))
tangent of (8x+9)^{-2}	tangent\:(8x+9)^{-2}
derivative of x^3-12x	\frac{d}{dx}(x^{3}-12x)
integral of (8(x^2+4))/(x(x^2+8))	\int\:\frac{8(x^{2}+4)}{x(x^{2}+8)}dx
derivative of 5x^3+3x^2-4x+1	\frac{d}{dx}(5x^{3}+3x^{2}-4x+1)
limit as x approaches 7+of 1/(x-7)	\lim\:_{x\to\:7+}(\frac{1}{x-7})
integral of e^{2x+4}	\int\:e^{2x+4}dx
derivative of f(x)=(\sqrt[3]{x})/(x-3)	derivative\:f(x)=\frac{\sqrt[3]{x}}{x-3}
(\partial)/(\partial x)(-x(2x-y^3))	\frac{\partial\:}{\partial\:x}(-x(2x-y^{3}))
derivative of 1/(x^{1/2})	\frac{d}{dx}(\frac{1}{x^{\frac{1}{2}}})
integral of ((x^2))/(sqrt(81-x^2))	\int\:\frac{(x^{2})}{\sqrt{81-x^{2}}}dx
derivative of (2x^3+1^2)	\frac{d}{dx}((2x^{3}+1)^{2})
slope ofintercept (2,6),(6,6)	slopeintercept\:(2,6),(6,6)
derivative of-6sin(x-3x)	\frac{d}{dx}(-6\sin(x)-3x)
integral of x^4(x^5-7)^6	\int\:x^{4}(x^{5}-7)^{6}dx
inverse oflaplace 8/(s-3)	inverselaplace\:\frac{8}{s-3}
derivative of 2sin(x+4cos(x))	\frac{d}{dx}(2\sin(x)+4\cos(x))
integral of 3t^5	\int\:3t^{5}dt
derivative of x^2cos(pix)	\frac{d}{dx}(x^{2}\cos(πx))
derivative of 5/(x-3)	\frac{d}{dx}(\frac{5}{x-3})
integral of-4cos(x)	\int\:-4\cos(x)dx
integral from 0 to 2 of e^{3x}	\int\:_{0}^{2}e^{3x}dx
integral of (5x^4-3x^2+2x+6)	\int\:(5x^{4}-3x^{2}+2x+6)dx
integral from 0 to 1 of 1/v	\int\:_{0}^{1}\frac{1}{v}dv

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