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Popular Calculus Problems

d/(dt)((\sqrt[3]{t})/(t-6))	\frac{d}{dt}(\frac{\sqrt[3]{t}}{t-6})
limit as x approaches 0 of x^4ln(x)	\lim\:_{x\to\:0}(x^{4}\ln(x))
slope of (-2.4)(2.4)	slope\:(-2.4)(2.4)
(\partial)/(\partial x)(2^{x^2})	\frac{\partial\:}{\partial\:x}(2^{x^{2}})
d/(dθ)(sqrt(1+cos(2θ)))	\frac{d}{dθ}(\sqrt{1+\cos(2θ)})
area x^2,6-x,[-3,2]	area\:x^{2},6-x,[-3,2]
tangent of y=\sqrt[4]{x},(1,1)	tangent\:y=\sqrt[4]{x},(1,1)
derivative of-2e^{3x}sin(2x)	\frac{d}{dx}(-2e^{3x}\sin(2x))
derivative of f(x)=(4x)/((x^3-6)^2)	derivative\:f(x)=\frac{4x}{(x^{3}-6)^{2}}
y^{''}+3y^'+y=1,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+3y^{\prime\:}+y=1,y(0)=1,y^{\prime\:}(0)=0
limit as x approaches 0 of ce^x+1	\lim\:_{x\to\:0}(ce^{x}+1)
integral of 1-1/x	\int\:1-\frac{1}{x}dx
integral of 6sin^3(xco)s^7x	\int\:6\sin^{3}(xco)s^{7}xdx
integral of 1/(x^2sqrt(x^2+81))	\int\:\frac{1}{x^{2}\sqrt{x^{2}+81}}dx
integral from-2 to 3 of (x+3)	\int\:_{-2}^{3}(x+3)dx
tangent of f(x)=x^2-2x+2,\at x=4	tangent\:f(x)=x^{2}-2x+2,\at\:x=4
derivative of ln((5x^2+3/(x^2)))	\frac{d}{dx}(\ln(\frac{5x^{2}+3}{x^{2}}))
3xy^'+7y=0,y(1)=8	3xy^{\prime\:}+7y=0,y(1)=8
integral of 2(2x+1)6	\int\:2(2x+1)6dx
y^{''}+8y^'-9y=0	y^{\prime\:\prime\:}+8y^{\prime\:}-9y=0
derivative of (z^2+e^z)sqrt(z)	derivative\:(z^{2}+e^{z})\sqrt{z}
(dy)/(dx)=-2y+x,y(0)=0	\frac{dy}{dx}=-2y+x,y(0)=0
derivative of sqrt(x)+x^2	\frac{d}{dx}(\sqrt{x}+x^{2})
integral of t^5	\int\:t^{5}dt
inverse oflaplace 1/(s(s+4)^2)	inverselaplace\:\frac{1}{s(s+4)^{2}}
derivative of (3x^2+5^3(3x-1)^2)	\frac{d}{dx}((3x^{2}+5)^{3}(3x-1)^{2})
integral of (1+x^2)^{-1}	\int\:(1+x^{2})^{-1}dx
tangent of f(x)=(e^{5x}-4)^2,(0,9)	tangent\:f(x)=(e^{5x}-4)^{2},(0,9)
derivative of sin(x-x*cos(x))	\frac{d}{dx}(\sin(x)-x\cdot\:\cos(x))
(dy)/(dx)+ycos(x)=sin(x)cos(x)	\frac{dy}{dx}+y\cos(x)=\sin(x)\cos(x)
derivative of-csc(x)-sin(x)	derivative\:-\csc(x)-\sin(x)
laplacetransform-6t^3	laplacetransform\:-6t^{3}
derivative of f(x)=x^3+6x^2+x	derivative\:f(x)=x^{3}+6x^{2}+x
y^{''}+2y^'+10y=3e^t+1	y^{\prime\:\prime\:}+2y^{\prime\:}+10y=3e^{t}+1
integral of 2050-18x-4x^2	\int\:2050-18x-4x^{2}dx
-y^'+(4y)/x =x^3y^2	-y^{\prime\:}+\frac{4y}{x}=x^{3}y^{2}
tangent of f(x)= 3/x ,\at x=-4	tangent\:f(x)=\frac{3}{x},\at\:x=-4
integral of (5+sqrt(x)+x)/x	\int\:\frac{5+\sqrt{x}+x}{x}dx
integral of ((3+x+x^2))/(sqrt(x))	\int\:\frac{(3+x+x^{2})}{\sqrt{x}}dx
limit as x approaches 2 of x^2-2x+4	\lim\:_{x\to\:2}(x^{2}-2x+4)
integral of cos(yx)	\int\:\cos(yx)dx
x(dy)/(dx)+2y=x^{-3}	x\frac{dy}{dx}+2y=x^{-3}
derivative of y=sqrt(e^{2x)+e^{-2x}}	derivative\:y=\sqrt{e^{2x}+e^{-2x}}
(dy)/(dx)=x+y,y(0)=0	\frac{dy}{dx}=x+y,y(0)=0
derivative of f(x)=3e^{-2x}ln(x)	derivative\:f(x)=3e^{-2x}\ln(x)
derivative of arcsin(5x^3)	\frac{d}{dx}(\arcsin(5x^{3}))
derivative of ln\|csc(3x\|)	\frac{d}{dx}(\ln\left\|\csc(3x)\right\|)
integral of 4e^{-0.4x}	\int\:4e^{-0.4x}dx
derivative of \sqrt[x]{(x+1)^2}	derivative\:\sqrt[x]{(x+1)^{2}}
tangent of (\|x\|)/(sqrt(5-x^2))	tangent\:\frac{\left\|x\right\|}{\sqrt{5-x^{2}}}
derivative of 6-e^{-x}	\frac{d}{dx}(6-e^{-x})
(dy)/(dx)=sqrt(7y)e^{x+3}	\frac{dy}{dx}=\sqrt{7y}e^{x+3}
derivative of (2^x^8)	\frac{d}{dx}((2^{x})^{8})
derivative of sqrt(x^2+e^{\sqrt{x)}}	\frac{d}{dx}(\sqrt{x^{2}+e^{\sqrt{x}}})
limit as x approaches 1 of (x+3)/2	\lim\:_{x\to\:1}(\frac{x+3}{2})
(\partial)/(\partial x)(3x^2-2y^3)	\frac{\partial\:}{\partial\:x}(3x^{2}-2y^{3})
(d^2)/(dx^2)(cos(x^2))	\frac{d^{2}}{dx^{2}}(\cos(x^{2}))
d/(dt)(1+y/t)	\frac{d}{dt}(1+\frac{y}{t})
integral of (x+3)sqrt(5-x)	\int\:(x+3)\sqrt{5-x}dx
derivative of f(x)= 1/(x^{1/2)}	derivative\:f(x)=\frac{1}{x^{\frac{1}{2}}}
integral of (162)/(x^2sqrt(81-x^2))	\int\:\frac{162}{x^{2}\sqrt{81-x^{2}}}dx
integral of (cos(8x))	\int\:(\cos(8x))dx
derivative of sqrt(x/(x^2+8))	\frac{d}{dx}(\sqrt{\frac{x}{x^{2}+8}})
sum from n=1 to infinity of n*x^n	\sum\:_{n=1}^{\infty\:}n\cdot\:x^{n}
derivative of 2-2cos(x)	\frac{d}{dx}(2-2\cos(x))
x(dy)/(dx)+xy=1	x\frac{dy}{dx}+xy=1
(\partial)/(\partial x)(e^{sqrt(5xy)})	\frac{\partial\:}{\partial\:x}(e^{\sqrt{5xy}})
integral of 1/(1+4t^2)	\int\:\frac{1}{1+4t^{2}}dt
(x+y)dx+x^2dy=0	(x+y)dx+x^{2}dy=0
(\partial)/(\partial x)(1(x-y)*e^{1y+4x^2})	\frac{\partial\:}{\partial\:x}(1(x-y)\cdot\:e^{1y+4x^{2}})
(d^3)/(dx^3)(sqrt(6x+3))	\frac{d^{3}}{dx^{3}}(\sqrt{6x+3})
integral from 0 to sin(x) of 8sqrt(t)	\int\:_{0}^{\sin(x)}8\sqrt{t}dt
integral of-x-3	\int\:-x-3dx
derivative of h(x)=(x^2-3)^3	derivative\:h(x)=(x^{2}-3)^{3}
integral from-8 to 2 of 1/(sqrt(\|2x\|))	\int\:_{-8}^{2}\frac{1}{\sqrt{\left\|2x\right\|}}dx
d/(dy)(sin(2y))	\frac{d}{dy}(\sin(2y))
y^{'''}-y^{''}-16y^'+16y=0	y^{\prime\:\prime\:\prime\:}-y^{\prime\:\prime\:}-16y^{\prime\:}+16y=0
limit as x approaches 0 of (sin^5(x))/x	\lim\:_{x\to\:0}(\frac{\sin^{5}(x)}{x})
(\partial)/(\partial y)(3x^2-5y)	\frac{\partial\:}{\partial\:y}(3x^{2}-5y)
y^'=(xy^2-0.5sin(2x))/(y(1-x^2))	y^{\prime\:}=\frac{xy^{2}-0.5\sin(2x)}{y(1-x^{2})}
y^{'''}+2y^{''}+y^'=0	y^{\prime\:\prime\:\prime\:}+2y^{\prime\:\prime\:}+y^{\prime\:}=0
limit as x approaches a of 9	\lim\:_{x\to\:a}(9)
inverse oflaplace (2s+1)/(s^2+2s+5)	inverselaplace\:\frac{2s+1}{s^{2}+2s+5}
tangent of y=x^2+x+3,\at x=3.99	tangent\:y=x^{2}+x+3,\at\:x=3.99
integral of xsec(2)(x)	\int\:x\sec(2)(x)dx
area x,0,2	area\:x,0,2
integral of x^{3/7}	\int\:x^{\frac{3}{7}}dx
inverse oflaplace (0.1)/(s+0.1)	inverselaplace\:\frac{0.1}{s+0.1}
d/(d{x)}({x}{z}+{x}{y}+{y}{z})	\frac{d}{d{x}}({x}{z}+{x}{y}+{y}{z})
integral from 2 to 3 of (x^4+1)/(x^5+5x)	\int\:_{2}^{3}\frac{x^{4}+1}{x^{5}+5x}dx
(ln(sqrt((1+x)/(1-x))))^'	(\ln(\sqrt{\frac{1+x}{1-x}}))^{\prime\:}
integral of ((x^2-1))/(x^2+1)	\int\:\frac{(x^{2}-1)}{x^{2}+1}dx
integral of 2x(x^2+1)^3	\int\:2x(x^{2}+1)^{3}dx
integral of sec^3(2x)tan(2x)	\int\:\sec^{3}(2x)\tan(2x)dx
derivative of x^2(1-x)^2	derivative\:x^{2}(1-x)^{2}
integral of x^2e^{-2x^2}	\int\:x^{2}e^{-2x^{2}}dx
area y=1-x^2,y=3-3x	area\:y=1-x^{2},y=3-3x
(\partial)/(\partial x)(2xy^4-2)	\frac{\partial\:}{\partial\:x}(2xy^{4}-2)
integral of (arcsin(x))	\int\:(\arcsin(x))dx
integral of (sin(2x))/(1+3sin^2(x))	\int\:\frac{\sin(2x)}{1+3\sin^{2}(x)}dx

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