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Popular Calculus Problems

inverse oflaplace 1-1/(1+x)	inverselaplace\:1-\frac{1}{1+x}
derivative of 4x^2sqrt(5x+1)	\frac{d}{dx}(4x^{2}\sqrt{5x+1})
integral of 5/(4sin(x)+3cos(x))	\int\:\frac{5}{4\sin(x)+3\cos(x)}dx
x^2y^{''}+2xy^'-6y=0,y(1)=0,y^'(1)=-4	x^{2}y^{\prime\:\prime\:}+2xy^{\prime\:}-6y=0,y(1)=0,y^{\prime\:}(1)=-4
derivative of 2/(\sqrt[4]{x^3)}	derivative\:\frac{2}{\sqrt[4]{x^{3}}}
derivative of sin(ln(4x^2))	\frac{d}{dx}(\sin(\ln(4)x^{2}))
derivative of y=xsqrt(400-x^2)	derivative\:y=x\sqrt{400-x^{2}}
derivative of x^5sin(2x)	\frac{d}{dx}(x^{5}\sin(2x))
derivative of (x^2(x+1^2)/(sqrt(x-1)))	\frac{d}{dx}(\frac{x^{2}(x+1)^{2}}{\sqrt{x-1}})
derivative of 6sqrt(4x^2+5)	derivative\:6\sqrt{4x^{2}+5}
derivative of e^{y-ln(x})	\frac{d}{dx}(e^{y-\ln(x)})
derivative of (x^4/(sqrt(x^5+3)))	\frac{d}{dx}(\frac{x^{4}}{\sqrt{x^{5}+3}})
(\partial)/(\partial y)(3x+y)	\frac{\partial\:}{\partial\:y}(3x+y)
integral of (23)/(23+e^x)	\int\:\frac{23}{23+e^{x}}dx
(\partial)/(\partial x)(xy+ln(x+y))	\frac{\partial\:}{\partial\:x}(xy+\ln(x+y))
derivative of sin^{ln(x}(3x))	\frac{d}{dx}(\sin^{\ln(x)}(3x))
integral of sin(sqrt(at))	\int\:\sin(\sqrt{at})dt
derivative of e^{3x}+10e^{2x}	\frac{d}{dx}(e^{3x}+10e^{2x})
t^2y^'+3ty+2t^3=0	t^{2}y^{\prime\:}+3ty+2t^{3}=0
(e^y+6x)dx+(xe^y)dy=0	(e^{y}+6x)dx+(xe^{y})dy=0
integral of e^{ln(2t)}	\int\:e^{\ln(2t)}dt
inverse oflaplace 1/((s+1)^2(s+2))	inverselaplace\:\frac{1}{(s+1)^{2}(s+2)}
tangent of-5/2 x^2+2x+2	tangent\:-\frac{5}{2}x^{2}+2x+2
integral of 3x^2y^2	\int\:3x^{2}y^{2}dx
integral from 3 to 5 of (x^4-3/(x^3))	\int\:_{3}^{5}(x^{4}-\frac{3}{x^{3}})dx
2(ln(y))y^'-x^5y=0	2(\ln(y))y^{\prime\:}-x^{5}y=0
derivative of y=cos(a^5+x^5)	derivative\:y=\cos(a^{5}+x^{5})
integral from 2 to 4 of 3/x	\int\:_{2}^{4}\frac{3}{x}dx
(\partial)/(\partial x)(2ysin(x)+e^{2z})	\frac{\partial\:}{\partial\:x}(2y\sin(x)+e^{2z})
limit as x approaches 0-of e^{-7/x}	\lim\:_{x\to\:0-}(e^{-\frac{7}{x}})
integral of-1/(2xsqrt(x^2+9))	\int\:-\frac{1}{2x\sqrt{x^{2}+9}}dx
derivative of e^{x^5}+log_{4}(pi)	derivative\:e^{x^{5}}+\log_{4}(π)
limit as n approaches infinity of a/n	\lim\:_{n\to\:\infty\:}(\frac{a}{n})
integral of ((x^2+1))/(2x)	\int\:\frac{(x^{2}+1)}{2x}dx
limit as x approaches 5-of (\|x-5\|)/(x-5)	\lim\:_{x\to\:5-}(\frac{\left\|x-5\right\|}{x-5})
derivative of (x^2/(7x+4))	\frac{d}{dx}(\frac{x^{2}}{7x+4})
(\partial)/(\partial y)(x^2*y)	\frac{\partial\:}{\partial\:y}(x^{2}\cdot\:y)
derivative of (4x/(6x-1))	\frac{d}{dx}(\frac{4x}{6x-1})
limit as x approaches 4 of sqrt(2x-7)	\lim\:_{x\to\:4}(\sqrt{2x-7})
integral of bx^2	\int\:bx^{2}dx
(2/((1+x)^3))^'	(\frac{2}{(1+x)^{3}})^{\prime\:}
sqrt(1-3x^2)(dy)/(dx)=x	\sqrt{1-3x^{2}}\frac{dy}{dx}=x
integral of 1+2x^2	\int\:1+2x^{2}dx
f(x)=3cos(3x)	f(x)=3\cos(3x)
derivative of-(6x/(6x^2+8))	\frac{d}{dx}(-\frac{6x}{6x^{2}+8})
integral from-3 to 2 of pi(y^2+2y+4)^2	\int\:_{-3}^{2}π(y^{2}+2y+4)^{2}dy
(dy)/(dx)= 1/(sqrt(1-x))	\frac{dy}{dx}=\frac{1}{\sqrt{1-x}}
integral of tcsc^2(t)	\int\:t\csc^{2}(t)dt
integral of 6xe^{-x}	\int\:6xe^{-x}dx
integral of 1/(sin(x)cos^5(x))	\int\:\frac{1}{\sin(x)\cos^{5}(x)}dx
derivative of x(x-7^2)	\frac{d}{dx}(x(x-7)^{2})
taylor ln(7-3x),2	taylor\:\ln(7-3x),2
derivative of 7/(4-3x)	\frac{d}{dx}(\frac{7}{4-3x})
derivative of cos^2(a-x)	\frac{d}{dx}(\cos^{2}(a-x))
derivative of f(x)=(x+x^3)/(sqrt(x))	derivative\:f(x)=\frac{x+x^{3}}{\sqrt{x}}
y^{''}-7y^'+12y=0,y(0)=1,y^'(0)=-2	y^{\prime\:\prime\:}-7y^{\prime\:}+12y=0,y(0)=1,y^{\prime\:}(0)=-2
limit as x approaches 4 of 5/(x-3)	\lim\:_{x\to\:4}(\frac{5}{x-3})
derivative of y=(x-2)/(sqrt(x)-\sqrt{2)}	derivative\:y=\frac{x-2}{\sqrt{x}-\sqrt{2}}
(\partial)/(\partial x)(2e^{5xy})	\frac{\partial\:}{\partial\:x}(2e^{5xy})
integral of tan(8x)	\int\:\tan(8x)dx
(\partial)/(\partial x)((y^2)/(1+x^2))	\frac{\partial\:}{\partial\:x}(\frac{y^{2}}{1+x^{2}})
((3x^2)/2)^'	(\frac{3x^{2}}{2})^{\prime\:}
d/(dy)((4x-2y)/(4x+2y))	\frac{d}{dy}(\frac{4x-2y}{4x+2y})
derivative of sqrt({r)(x(x)^2-x^2})	\frac{d}{dx}(\sqrt{{r}(x)(x)^{2}-x^{2}})
derivative of (1+e^x^3)	\frac{d}{dx}((1+e^{x})^{3})
laplacetransform e^{-2t}cos(3t)	laplacetransform\:e^{-2t}\cos(3t)
(\partial)/(\partial x)(xe^y+x^4y+y^3)	\frac{\partial\:}{\partial\:x}(xe^{y}+x^{4}y+y^{3})
derivative of ln(x^2+y^4)	\frac{d}{dx}(\ln(x^{2}+y^{4}))
laplacetransform 4cos(5t)	laplacetransform\:4\cos(5t)
y^'+y=3	y^{\prime\:}+y=3
partialfraction (5x)/(x-2)	partialfraction\:\frac{5x}{x-2}
y^'=6xsqrt(9-y^2)	y^{\prime\:}=6x\sqrt{9-y^{2}}
y^'=1+x+y^2+xy^2	y^{\prime\:}=1+x+y^{2}+xy^{2}
limit as x approaches infinity of (3^{x+4})/(8^x)	\lim\:_{x\to\:\infty\:}(\frac{3^{x+4}}{8^{x}})
derivative of (x^4+y^4/(xy))	\frac{d}{dx}(\frac{x^{4}+y^{4}}{xy})
tangent of f(x)=-3x^2-2x,\at x=2	tangent\:f(x)=-3x^{2}-2x,\at\:x=2
sum from n=0 to infinity of (4/10)^n	\sum\:_{n=0}^{\infty\:}(\frac{4}{10})^{n}
integral from 2 to 3 of 21t^2	\int\:_{2}^{3}21t^{2}dt
sum from n=1 to infinity}(n^4x^{3n of)/(5^{3n)}	\sum\:_{n=1}^{\infty\:}\frac{n^{4}x^{3n}}{5^{3n}}
derivative of 4x+12y,12x-3y	\frac{d}{dx}(4x+12y,12x-3y)
f(r)=6\sqrt[3]{r}	f(r)=6\sqrt[3]{r}
integral of x^2*sin(3x)	\int\:x^{2}\cdot\:\sin(3x)dx
limit as x approaches 14 of 7/x+sqrt(x)	\lim\:_{x\to\:14}(\frac{7}{x}+\sqrt{x})
inverse oflaplace (3s)/(s^2+5s+6)	inverselaplace\:\frac{3s}{s^{2}+5s+6}
tangent of 8cos(x)	tangent\:8\cos(x)
integral of y/(sqrt(y^2+1))	\int\:\frac{y}{\sqrt{y^{2}+1}}dy
(x+y)dx+(x+y-4)dy=0	(x+y)dx+(x+y-4)dy=0
integral of x^{-1}e^x	\int\:x^{-1}e^{x}dx
derivative of (8x/(x+5))	\frac{d}{dx}(\frac{8x}{x+5})
derivative of (3x^2-4x)e^x	derivative\:(3x^{2}-4x)e^{x}
integral of 1/(tsqrt(2t^2-9))	\int\:\frac{1}{t\sqrt{2t^{2}-9}}dt
limit as x approaches 0 of ((tan(3x)))/x	\lim\:_{x\to\:0}(\frac{(\tan(3x))}{x})
(\partial)/(\partial y)(sin(x^2-y))	\frac{\partial\:}{\partial\:y}(\sin(x^{2}-y))
integral of (tan^3(x))	\int\:(\tan^{3}(x))dx
area y=x^2,y=x+2,0	area\:y=x^{2},y=x+2,0
area y= x/(x^2-4x+5),y= 3/(x^2-4x+5),x=0	area\:y=\frac{x}{x^{2}-4x+5},y=\frac{3}{x^{2}-4x+5},x=0
slope of y=(x^3+1)/(6x),x=1	slope\:y=\frac{x^{3}+1}{6x},x=1
y^'+4y=e^{-x},y(0)=10	y^{\prime\:}+4y=e^{-x},y(0)=10
integral from 0 to 6 of 1/(sqrt(\|x-3\|))	\int\:_{0}^{6}\frac{1}{\sqrt{\left\|x-3\right\|}}dx
derivative of x(x^2+3^3)	\frac{d}{dx}(x(x^{2}+3)^{3})

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