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Popular Calculus Problems

derivative of (csc(x)/(1+csc(x)))	\frac{d}{dx}(\frac{\csc(x)}{1+\csc(x)})
y^{''}+4y=e^{4x}	y^{\prime\:\prime\:}+4y=e^{4x}
integral of e^{e^x}	\int\:e^{e^{x}}dx
derivative of (2x-1/(x-1))	\frac{d}{dx}(\frac{2x-1}{x-1})
(\partial)/(\partial x)(-xe^{-xy})	\frac{\partial\:}{\partial\:x}(-xe^{-xy})
integral of (31x^2)/(sqrt(x^2-4))	\int\:\frac{31x^{2}}{\sqrt{x^{2}-4}}dx
laplacetransform-1	laplacetransform\:-1
(\partial)/(\partial y)(xe^xsin(y))	\frac{\partial\:}{\partial\:y}(xe^{x}\sin(y))
tangent of (3x^4-12)^{1/2}	tangent\:(3x^{4}-12)^{\frac{1}{2}}
derivative of 2x^2+7x+4	derivative\:2x^{2}+7x+4
integral of xcos(3pi)x^2	\int\:x\cos(3π)x^{2}dx
laplacetransform 10+t^2	laplacetransform\:10+t^{2}
(\partial)/(\partial y)(6x^2)	\frac{\partial\:}{\partial\:y}(6x^{2})
integral of (6+x^2)/x	\int\:\frac{6+x^{2}}{x}dx
derivative of (x+1)(7sqrt(x)+2)	derivative\:(x+1)(7\sqrt{x}+2)
(\partial)/(\partial x)(x/(y^2)+xy+8)	\frac{\partial\:}{\partial\:x}(\frac{x}{y^{2}}+xy+8)
derivative of ln(((2x+1^3)/((3x-1)^4)))	\frac{d}{dx}(\ln(\frac{(2x+1)^{3}}{(3x-1)^{4}}))
taylor z(z+1)e^z	taylor\:z(z+1)e^{z}
area f(x)=16-x^2,(1,4)	area\:f(x)=16-x^{2},(1,4)
(\partial)/(\partial x)((2xy-1)e^{-xy})	\frac{\partial\:}{\partial\:x}((2xy-1)e^{-xy})
derivative of e^{2(x-1^2}+x/(1+x^3))	\frac{d}{dx}(e^{2(x-1)^{2}}+\frac{x}{1+x^{3}})
(9+y^2)dx+4xydy=0	(9+y^{2})dx+4xydy=0
tangent of y=8x+12-15e^x,(0,-3)	tangent\:y=8x+12-15e^{x},(0,-3)
integral of (3+x)/(1+x^2)	\int\:\frac{3+x}{1+x^{2}}dx
area x^2+10,9x,0	area\:x^{2}+10,9x,0
integral of ((9-y^2)^2)/2-y(9-y^2)	\int\:\frac{(9-y^{2})^{2}}{2}-y(9-y^{2})dy
integral of sqrt(y+4)	\int\:\sqrt{y+4}dy
derivative of (2x/(x^4+1))	\frac{d}{dx}(\frac{2x}{x^{4}+1})
integral from 1 to 4 of-10sqrt(t)ln(t)	\int\:_{1}^{4}-10\sqrt{t}\ln(t)dt
integral of 10x^5e^{-x^3}	\int\:10x^{5}e^{-x^{3}}dx
derivative of-3x^2+2	\frac{d}{dx}(-3x^{2}+2)
roots Ax+B	roots\:Ax+B
inverse oflaplace e^{-,\at}	inverselaplace\:e^{-,\at\:}
integral of 4/(3-e^x)	\int\:\frac{4}{3-e^{x}}dx
area x^2+2x+11,-4x+2,[0]	area\:x^{2}+2x+11,-4x+2,[0]
integral of 3/(1-x^2)	\int\:\frac{3}{1-x^{2}}dx
(\partial)/(\partial x)(x^4+y^4-4x^2y^2)	\frac{\partial\:}{\partial\:x}(x^{4}+y^{4}-4x^{2}y^{2})
(\partial)/(\partial y)(y/(x^2y^2+1))	\frac{\partial\:}{\partial\:y}(\frac{y}{x^{2}y^{2}+1})
integral of \sqrt[6]{3}+\sqrt[6]{x}	\int\:\sqrt[6]{3}+\sqrt[6]{x}dx
taylor x^2+x^3	taylor\:x^{2}+x^{3}
integral of e^{t-s}	\int\:e^{t-s}ds
derivative of 2pi^2	\frac{d}{dx}(2π^{2})
integral of (x^4)/(x+1)	\int\:\frac{x^{4}}{x+1}dx
integral of tsqrt(t)	\int\:t\sqrt{t}dt
integral of (e^{-t})	\int\:(e^{-t})dt
integral from 1/2 to 1 of (y+4)/(y^2+y)	\int\:_{\frac{1}{2}}^{1}\frac{y+4}{y^{2}+y}dy
derivative of y=0.7(1.02)^x	derivative\:y=0.7(1.02)^{x}
derivative of f(x)=1-4x^2	derivative\:f(x)=1-4x^{2}
(dy)/(dx)=y(0.1-10^{-7}y)	\frac{dy}{dx}=y(0.1-10^{-7}y)
derivative of ln\|x-1\|-ln\|x-3\|	\frac{d}{dx}(\ln\left\|x-1\right\|-\ln\left\|x-3\right\|)
integral of arccsc(t/2)	\int\:\arccsc(\frac{t}{2})dt
limit as x approaches 2 of x^2	\lim\:_{x\to\:2}(x^{2})
derivative of (7a+1)^2	derivative\:(7a+1)^{2}
limit as x approaches 9 of 4/(x-9)	\lim\:_{x\to\:9}(\frac{4}{x-9})
integral from 0 to 2 of (5x-15)/(2x-3)	\int\:_{0}^{2}\frac{5x-15}{2x-3}dx
derivative of y=x^2arctan(5x)	derivative\:y=x^{2}\arctan(5x)
derivative of x*sin(x)	derivative\:x\cdot\:\sin(x)
(dy)/(dx)=kx	\frac{dy}{dx}=kx
integral of (18x^3-36x^2+4)/(x^2-2x)	\int\:\frac{18x^{3}-36x^{2}+4}{x^{2}-2x}dx
maclaurin e^{8x}	maclaurin\:e^{8x}
slope of (-2,-2),(-1,2)	slope\:(-2,-2),(-1,2)
(\partial)/(\partial x)(e^{x^2-y^2+4y})	\frac{\partial\:}{\partial\:x}(e^{x^{2}-y^{2}+4y})
integral from 1 to 4 of (x^2-2)	\int\:_{1}^{4}(x^{2}-2)dx
f(x)=3sin(3x)	f(x)=3\sin(3x)
integral of 1/(x^2(x-1)^2)	\int\:\frac{1}{x^{2}(x-1)^{2}}dx
derivative of 3x^5-30x^3	\frac{d}{dx}(3x^{5}-30x^{3})
f(x)=5x^2-3x+7	f(x)=5x^{2}-3x+7
(\partial}{\partial x}(\frac{x^3)/3+4y)	\frac{\partial\:}{\partial\:x}(\frac{x^{3}}{3}+4y)
(dy)/(dx)=x^6y^{-7}	\frac{dy}{dx}=x^{6}y^{-7}
derivative of sqrt(1-y^2)	derivative\:\sqrt{1-y^{2}}
(dy)/(dx)=x^8e^{x^9}	\frac{dy}{dx}=x^{8}e^{x^{9}}
y^{''}+25y=-10sin(5t)	y^{\prime\:\prime\:}+25y=-10\sin(5t)
limit as x approaches a+1 of x^2-1	\lim\:_{x\to\:a+1}(x^{2}-1)
d/(dy)(1/(sqrt(x^2+y^2)))	\frac{d}{dy}(\frac{1}{\sqrt{x^{2}+y^{2}}})
derivative of 1-4x^2	\frac{d}{dx}(1-4x^{2})
integral of sqrt(64-t^2)	\int\:\sqrt{64-t^{2}}dt
derivative of-6e^{-x}	\frac{d}{dx}(-6e^{-x})
integral of 8/(sqrt(x^2-36))	\int\:\frac{8}{\sqrt{x^{2}-36}}dx
derivative of e^6+ln(9)	\frac{d}{dx}(e^{6}+\ln(9))
tangent of f(x)^8x^2+4x-7,x=-3	tangent\:f(x)^{8}x^{2}+4x-7,x=-3
integral of sec^2(xta)n^5x	\int\:\sec^{2}(xta)n^{5}xdx
derivative of (1/(y^2)-5/(y^4))(y+3y^3)	derivative\:(\frac{1}{y^{2}}-\frac{5}{y^{4}})(y+3y^{3})
limit as x approaches 3+of 18ln(x-3)	\lim\:_{x\to\:3+}(18\ln(x-3))
derivative of e^5	\frac{d}{dx}(e^{5})
integral of (tan(x))/x	\int\:\frac{\tan(x)}{x}dx
laplacetransform e^{-t}t^2	laplacetransform\:e^{-t}t^{2}
integral of 2xsqrt(2-x^2)	\int\:2x\sqrt{2-x^{2}}dx
derivative of (x^3+x/(x^4-2))	\frac{d}{dx}(\frac{x^{3}+x}{x^{4}-2})
derivative of y=2e^{-x}+e^{3x}	derivative\:y=2e^{-x}+e^{3x}
sum from n=1 to infinity of n/(4n^3+1)	\sum\:_{n=1}^{\infty\:}\frac{n}{4n^{3}+1}
derivative of h(x)=sec^6(x)	derivative\:h(x)=\sec^{6}(x)
integral of (e^x)/(sqrt(1-25e^{2x))}	\int\:\frac{e^{x}}{\sqrt{1-25e^{2x}}}dx
(\partial)/(\partial x)(x/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{2}+y^{2}})
derivative of 3sin^3(sqrt(x))	\frac{d}{dx}(3\sin^{3}(\sqrt{x}))
(\partial)/(\partial x)(ln(x+5y+3z))	\frac{\partial\:}{\partial\:x}(\ln(x+5y+3z))
(\partial)/(\partial x)(x^3+3xy^2-3x)	\frac{\partial\:}{\partial\:x}(x^{3}+3xy^{2}-3x)
integral from 2.5 to 0.5 of (23.75-7.5v)	\int\:_{2.5}^{0.5}(23.75-7.5v)dv
(\partial)/(\partial y)(8x-(x+y)^3)	\frac{\partial\:}{\partial\:y}(8x-(x+y)^{3})
derivative of sqrt(1/(x^{31)})	\frac{d}{dx}(\sqrt{\frac{1}{x^{31}}})
derivative of (2/(sqrt(x))-1)^{-1}	derivative\:(\frac{2}{\sqrt{x}}-1)^{-1}

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