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Popular Calculus Problems

derivative of f(t)=e^{4tsin(2t)}	derivative\:f(t)=e^{4t\sin(2t)}
integral of (sin(2x))/(x^2)	\int\:\frac{\sin(2x)}{x^{2}}dx
integral of x^3ln(6x)	\int\:x^{3}\ln(6x)dx
integral of (y-1)/(y+4)	\int\:\frac{y-1}{y+4}dy
integral of 8sec^3(6x)	\int\:8\sec^{3}(6x)dx
(\partial)/(\partial x)(3e^{2x}-5ln(y)+7)	\frac{\partial\:}{\partial\:x}(3e^{2x}-5\ln(y)+7)
integral from 2 to 7 of x	\int\:_{2}^{7}xdx
(dy)/(dx)=((3y+2)/(5x+4))^2	\frac{dy}{dx}=(\frac{3y+2}{5x+4})^{2}
integral of ln(sqrt(2x))	\int\:\ln(\sqrt{2x})dx
(\partial)/(\partial x)(sin(4x))	\frac{\partial\:}{\partial\:x}(\sin(4x))
derivative of (7x/(x^2+4))	\frac{d}{dx}(\frac{7x}{x^{2}+4})
derivative of 1/6 x^3+1/(2x)	derivative\:\frac{1}{6}x^{3}+\frac{1}{2x}
derivative of sqrt(4+3{f)(x})	\frac{d}{dx}(\sqrt{4+3{f}(x)})
laplacetransform e^{4t}	laplacetransform\:e^{4t}
limit as x approaches 0 of (2/x)^x	\lim\:_{x\to\:0}((\frac{2}{x})^{x})
limit as x approaches 4+of 4sqrt(x-4)	\lim\:_{x\to\:4+}(4\sqrt{x-4})
(\partial)/(\partial x)(e^{3x}sin(3y))	\frac{\partial\:}{\partial\:x}(e^{3x}\sin(3y))
derivative of c_{1}e^x+c_{2}xe^x	\frac{d}{dx}(c_{1}e^{x}+c_{2}xe^{x})
sum from n=0 to infinity of 1/(10^n)	\sum\:_{n=0}^{\infty\:}\frac{1}{10^{n}}
y^'+7y=t+e^{-2t}	y^{\prime\:}+7y=t+e^{-2t}
limit as x approaches 0+of x^3+3x+2	\lim\:_{x\to\:0+}(x^{3}+3x+2)
integral of 2/(x^2+2x+2)	\int\:\frac{2}{x^{2}+2x+2}dx
limit as x approaches 1 of (x-1)/(x^2-1)	\lim\:_{x\to\:1}(\frac{x-1}{x^{2}-1})
derivative of x^3(ln(x)^{cos(x)})	\frac{d}{dx}(x^{3}(\ln(x))^{\cos(x)})
integral of y^{-4}	\int\:y^{-4}dy
tangent of f(x)= 3/((x+5)^2),\at x= 3/16	tangent\:f(x)=\frac{3}{(x+5)^{2}},\at\:x=\frac{3}{16}
(\partial)/(\partial y)((5x)/(6y))	\frac{\partial\:}{\partial\:y}(\frac{5x}{6y})
(cot(x))^'	(\cot(x))^{\prime\:}
(\partial)/(\partial x)(tan(3x-4y))	\frac{\partial\:}{\partial\:x}(\tan(3x-4y))
integral of 3/(u^2+2)	\int\:\frac{3}{u^{2}+2}du
derivative of f(x)=(2x-x^2)^3	derivative\:f(x)=(2x-x^{2})^{3}
y^'=3-(2y)	y^{\prime\:}=3-(2y)
(\partial)/(\partial y)(ln(x^2+y^3))	\frac{\partial\:}{\partial\:y}(\ln(x^{2}+y^{3}))
simplify (x-5)/(sqrt(x))	simplify\:\frac{x-5}{\sqrt{x}}
integral from 4 to 9 of 1/2 y^{1/2}+1/2 y^{-1/2}	\int\:_{4}^{9}\frac{1}{2}y^{\frac{1}{2}}+\frac{1}{2}y^{-\frac{1}{2}}dy
derivative of a(2e^{-2x}x-2e^{-2x}x^2)	\frac{d}{dx}(a(2e^{-2x}x-2e^{-2x}x^{2}))
integral from-2 to 4 of x+2	\int\:_{-2}^{4}x+2dx
(\partial)/(\partial y)(-y/(y^2+x^2))	\frac{\partial\:}{\partial\:y}(-\frac{y}{y^{2}+x^{2}})
integral from 0 to 6 of 36-x^2	\int\:_{0}^{6}36-x^{2}dx
limit as x approaches 0+of ln(ln(x))	\lim\:_{x\to\:0+}(\ln(\ln(x)))
(dy)/(dx)= 1/(sec^2(y))	\frac{dy}{dx}=\frac{1}{\sec^{2}(y)}
derivative of (x^4+2/(ln(x)))	\frac{d}{dx}(\frac{x^{4}+2}{\ln(x)})
integral of x/(e^{4x)}	\int\:\frac{x}{e^{4x}}dx
sum from n=1 to infinity of 2/(9^n)	\sum\:_{n=1}^{\infty\:}\frac{2}{9^{n}}
tangent of 3x-2x^2	tangent\:3x-2x^{2}
limit as x approaches 0 of (e^{-1/x})^x	\lim\:_{x\to\:0}((e^{-\frac{1}{x}})^{x})
integral of xe^{2xy}	\int\:xe^{2xy}dy
(\partial)/(\partial y)(3x^2y+4xy^2)	\frac{\partial\:}{\partial\:y}(3x^{2}y+4xy^{2})
integral of e^{-x/(10)}	\int\:e^{-\frac{x}{10}}dx
derivative of 20-2x	\frac{d}{dx}(20-2x)
derivative of (x^4/8 ln(x)-(x^4)/(32))	\frac{d}{dx}(\frac{x^{4}}{8}\ln(x)-\frac{x^{4}}{32})
tangent of y= 8/(x+1)	tangent\:y=\frac{8}{x+1}
limit as x approaches 0 of x*e^{1/x}	\lim\:_{x\to\:0}(x\cdot\:e^{\frac{1}{x}})
derivative of (cos(2x)/x)	\frac{d}{dx}(\frac{\cos(2x)}{x})
(\partial)/(\partial x)(ln(((x+y))/(x-y)))	\frac{\partial\:}{\partial\:x}(\ln(\frac{(x+y)}{x-y}))
derivative of ((6e^x)/(2e^x+1))	\frac{d}{dx}(\frac{(6e^{x})}{2e^{x}+1})
integral of 1/(xsqrt(121x^2-121))	\int\:\frac{1}{x\sqrt{121x^{2}-121}}dx
integral of y+x	\int\:y+xdx
(\partial)/(\partial x)(in(x+2y+3z))	\frac{\partial\:}{\partial\:x}(in(x+2y+3z))
integral of ((ln(x))^{48})/x	\int\:\frac{(\ln(x))^{48}}{x}dx
derivative of ln(3-5x)	derivative\:\ln(3-5x)
derivative of (3tan(x)/x)	\frac{d}{dx}(\frac{3\tan(x)}{x})
derivative of f(x)=((ax+b))/(cx+d)	derivative\:f(x)=\frac{(ax+b)}{cx+d}
derivative of 1/8 y^3	derivative\:\frac{1}{8}y^{3}
(d^2)/(dx^2)(5csc(x))	\frac{d^{2}}{dx^{2}}(5\csc(x))
maclaurin ln((sqrt(1+2x))/(1-3x))	maclaurin\:\ln(\frac{\sqrt{1+2x}}{1-3x})
slope of (4.5)(1.2)	slope\:(4.5)(1.2)
derivative of (x^3/(sin(x)))	\frac{d}{dx}(\frac{x^{3}}{\sin(x)})
((x^2+1)dy)/(dx)+7x(y-1)=0	\frac{(x^{2}+1)dy}{dx}+7x(y-1)=0
integral of sqrt(x)*(3x+sqrt(x))	\int\:\sqrt{x}\cdot\:(3x+\sqrt{x})dx
(\partial)/(\partial x)(e^{4x})	\frac{\partial\:}{\partial\:x}(e^{4x})
integral of-1/(e^{3x)}	\int\:-\frac{1}{e^{3x}}dx
integral of 5cos^3(5x)	\int\:5\cos^{3}(5x)dx
(\partial)/(\partial x)(cos^9(x^8y^6))	\frac{\partial\:}{\partial\:x}(\cos^{9}(x^{8}y^{6}))
derivative of 4^{c/x}	derivative\:4^{\frac{c}{x}}
integral from 0 to infinity of xe^{-x/9}	\int\:_{0}^{\infty\:}xe^{-\frac{x}{9}}dx
limit as x approaches infinity of-3	\lim\:_{x\to\:\infty\:}(-3)
(\partial)/(\partial x)((3x+2xy)/(7x+6y))	\frac{\partial\:}{\partial\:x}(\frac{3x+2xy}{7x+6y})
integral of 6tan^3(x)	\int\:6\tan^{3}(x)dx
limit as x approaches 0 of x*ln(sin(x))	\lim\:_{x\to\:0}(x\cdot\:\ln(\sin(x)))
derivative of (4x/(sqrt(x^2+6)))	\frac{d}{dx}(\frac{4x}{\sqrt{x^{2}+6}})
ydx-(4x^2y+x)dy=0	ydx-(4x^{2}y+x)dy=0
derivative of ln(xe^{-7x})	\frac{d}{dx}(\ln(xe^{-7x}))
integral from 1.5 to 2.5 of 9800(7-y)(1)	\int\:_{1.5}^{2.5}9800(7-y)(1)dy
inverse oflaplace 1/(s^2+16)	inverselaplace\:\frac{1}{s^{2}+16}
inverse oflaplace 1/(s(s^2+s+5/4))	inverselaplace\:\frac{1}{s(s^{2}+s+\frac{5}{4})}
derivative of e^{x-1}	derivative\:e^{x-1}
(\partial)/(\partial x)(2xy+5x^2)	\frac{\partial\:}{\partial\:x}(2xy+5x^{2})
tangent of f(x)=(x^2)/(x+9),\at x=1	tangent\:f(x)=\frac{x^{2}}{x+9},\at\:x=1
limit as x approaches 0 of x/(x^2+5x)	\lim\:_{x\to\:0}(\frac{x}{x^{2}+5x})
derivative of y=x^4f(x)	derivative\:y=x^{4}f(x)
inverse oflaplace 6/(2s+1)	inverselaplace\:\frac{6}{2s+1}
integral of cot(x)ln(sin(x))	\int\:\cot(x)\ln(\sin(x))dx
derivative of (x-2/(x^2+5x+4))	\frac{d}{dx}(\frac{x-2}{x^{2}+5x+4})
(dy)/(dx)=-y^{1/3}	\frac{dy}{dx}=-y^{\frac{1}{3}}
limit as x approaches 0 of pi^2	\lim\:_{x\to\:0}(π^{2})
integral of-1/2 cos(2t)	\int\:-\frac{1}{2}\cos(2t)dt
integral of 3sec(2x)tan(2x)	\int\:3\sec(2x)\tan(2x)dx
integral of xcos(7x)	\int\:x\cos(7x)dx
derivative of 3-2x	\frac{d}{dx}(3-2x)

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