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Popular Calculus Problems

derivative of 6e^x	derivative\:6e^{x}
(dy)/(dx)=5y+a	\frac{dy}{dx}=5y+a
integral of (x^2+4x)	\int\:(x^{2}+4x)dx
inverse oflaplace 4/((s+1)(s+2)^3)	inverselaplace\:\frac{4}{(s+1)(s+2)^{3}}
derivative of (5x+2/(3x-4))	\frac{d}{dx}(\frac{5x+2}{3x-4})
inverse oflaplace 1/((s-1)^2(s+5))	inverselaplace\:\frac{1}{(s-1)^{2}(s+5)}
tangent of f(x)=sin(sin(x)),\at x=4pi	tangent\:f(x)=\sin(\sin(x)),\at\:x=4π
y^'=y(1-y)	y^{\prime\:}=y(1-y)
derivative of y=e^{4x^2}+1	derivative\:y=e^{4x^{2}}+1
tangent of f(x)=tan(x),\at x=1	tangent\:f(x)=\tan(x),\at\:x=1
area 19x,x^2	area\:19x,x^{2}
sum from n=0 to infinity of 1/3 (2/3)^n	\sum\:_{n=0}^{\infty\:}\frac{1}{3}(\frac{2}{3})^{n}
derivative of y=log_{10}(x)	derivative\:y=\log_{10}(x)
limit as x approaches 5-of (\|5-x\|)/(5-x)	\lim\:_{x\to\:5-}(\frac{\left\|5-x\right\|}{5-x})
taylor ((e^x-1))/x	taylor\:\frac{(e^{x}-1)}{x}
integral of (-3)/(x^2)	\int\:\frac{-3}{x^{2}}dx
y^'=ycos(x)	y^{\prime\:}=y\cos(x)
y^'+y/x =y^2	y^{\prime\:}+\frac{y}{x}=y^{2}
(\partial)/(\partial y)(50x+400-50y)	\frac{\partial\:}{\partial\:y}(50x+400-50y)
derivative of 8e^{-x}+1	derivative\:8e^{-x}+1
derivative of ln((6-x/(6+x)))	\frac{d}{dx}(\ln(\frac{6-x}{6+x}))
(\partial)/(\partial x)(y-2x)	\frac{\partial\:}{\partial\:x}(y-2x)
integral of 12sin^2(x)	\int\:12\sin^{2}(x)dx
x^{''}+x^'+2x=4e^{2t}	x^{\prime\:\prime\:}+x^{\prime\:}+2x=4e^{2t}
derivative of x^{x^{1/2}}	\frac{d}{dx}(x^{x^{\frac{1}{2}}})
f(x)=9e^x	f(x)=9e^{x}
(dy)/(dx)=((x^3+y^3))/(xy^2)	\frac{dy}{dx}=\frac{(x^{3}+y^{3})}{xy^{2}}
sum from k=1 to infinity of 3(1/5)^{k-1}	\sum\:_{k=1}^{\infty\:}3(\frac{1}{5})^{k-1}
(\partial)/(\partial y)(-2)	\frac{\partial\:}{\partial\:y}(-2)
derivative of 2/((1+x)^3)	derivative\:\frac{2}{(1+x)^{3}}
limit as x approaches 0 of (x-1)/(x^2)	\lim\:_{x\to\:0}(\frac{x-1}{x^{2}})
tangent of 3/x+5/(x^3),\at x=-1	tangent\:\frac{3}{x}+\frac{5}{x^{3}},\at\:x=-1
derivative of x/(sqrt(x-3))	\frac{d}{dx}(\frac{x}{\sqrt{x-3}})
(\partial)/(\partial x)(sqrt(x^2+y^2+z^2))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+y^{2}+z^{2}})
integral of 2/((1-x)^2)	\int\:\frac{2}{(1-x)^{2}}dx
taylor ln(1+2x),0	taylor\:\ln(1+2x),0
taylor (cos^2(2θ))/(cos(θ))	taylor\:\frac{\cos^{2}(2θ)}{\cos(θ)}
integral of 14x^{15}e^{x^8}	\int\:14x^{15}e^{x^{8}}dx
integral of (x-2)sin(pix)	\int\:(x-2)\sin(πx)dx
y^{''}+6y^'+25y=0,y(0)=2,y^'(0)=-3	y^{\prime\:\prime\:}+6y^{\prime\:}+25y=0,y(0)=2,y^{\prime\:}(0)=-3
derivative of (4x+sqrt(1+x)/(x^2-1))	\frac{d}{dx}(\frac{4x+\sqrt{1+x}}{x^{2}-1})
derivative of ln(sec(5x)+tan(5x))	derivative\:\ln(\sec(5x)+\tan(5x))
integral of 5(cos(x)+sin(2x))/(sin(x))	\int\:5\frac{\cos(x)+\sin(2x)}{\sin(x)}dx
sum from n=1 to infinity of 8(-1/4)^n	\sum\:_{n=1}^{\infty\:}8(-\frac{1}{4})^{n}
limit as x approaches 0+of 2sqrt(x)ln(x)	\lim\:_{x\to\:0+}(2\sqrt{x}\ln(x))
x^2+4,-x^2-1,x=-2,x=3	x^{2}+4,-x^{2}-1,x=-2,x=3
f(x)=x^2ln(2x)	f(x)=x^{2}\ln(2x)
xy^'=y+5x^2sin(x)	xy^{\prime\:}=y+5x^{2}\sin(x)
derivative of f(x)=(2x^3+6x)(4x^2-7x+11)	derivative\:f(x)=(2x^{3}+6x)(4x^{2}-7x+11)
derivative of (x^2/(sqrt(x^2-4)))	\frac{d}{dx}(\frac{x^{2}}{\sqrt{x^{2}-4}})
(\partial)/(\partial y)((x+y)/(xy-1))	\frac{\partial\:}{\partial\:y}(\frac{x+y}{xy-1})
integral of (x^2+3)/(sqrt(x))	\int\:\frac{x^{2}+3}{\sqrt{x}}dx
tangent of 2x(5-4x)^4,\at x=1	tangent\:2x(5-4x)^{4},\at\:x=1
(-3xy^2+5y)+(-3x^2y+5x)y^'=0	(-3xy^{2}+5y)+(-3x^{2}y+5x)y^{\prime\:}=0
derivative of (x^2-4^{1/2})	\frac{d}{dx}((x^{2}-4)^{\frac{1}{2}})
integral of p^2	\int\:p^{2}dp
limit as x approaches-2 of 1/(x+2)	\lim\:_{x\to\:-2}(\frac{1}{x+2})
simplify e^4	simplify\:e^{4}
integral of 1/((x^3-4x))	\int\:\frac{1}{(x^{3}-4x)}dx
d/(dθ)(1+cos(2θ))	\frac{d}{dθ}(1+\cos(2θ))
limit as x approaches-1-of x/((x+1)^2)	\lim\:_{x\to\:-1-}(\frac{x}{(x+1)^{2}})
(2cos(2x))^'	(2\cos(2x))^{\prime\:}
inverse oflaplace 3s+2	inverselaplace\:3s+2
limit as x approaches infinity of e^x-3	\lim\:_{x\to\:\infty\:}(e^{x}-3)
derivative of ({z}(x)/x)	\frac{d}{dx}(\frac{{z}(x)}{x})
integral from 0 to 2 of (y-2)^2	\int\:_{0}^{2}(y-2)^{2}dy
derivative of (2x+1^2(x^2+x+1))	\frac{d}{dx}((2x+1)^{2}(x^{2}+x+1))
integral of 1/((x+6)^2)	\int\:\frac{1}{(x+6)^{2}}dx
derivative of (2x^2-5x+7^3)	\frac{d}{dx}((2x^{2}-5x+7)^{3})
integral of θsin(θ)	\int\:θ\sin(θ)dθ
derivative of (2x^2+2x+2/(sqrt(x)))	\frac{d}{dx}(\frac{2x^{2}+2x+2}{\sqrt{x}})
derivative of ln(ln(3x))	derivative\:\ln(\ln(3x))
derivative of (x+2/(x^2+2x+4))	\frac{d}{dx}(\frac{x+2}{x^{2}+2x+4})
x^3y^{'''}-6y=0	x^{3}y^{\prime\:\prime\:\prime\:}-6y=0
integral of (6sin(2x))/(sin(x))	\int\:\frac{6\sin(2x)}{\sin(x)}dx
integral of sec^2(θ)+7	\int\:\sec^{2}(θ)+7dθ
area y= 5/6 x^2,y= 11/6-x^2	area\:y=\frac{5}{6}x^{2},y=\frac{11}{6}-x^{2}
derivative of e^{rx}r	\frac{d}{dx}(e^{rx}r)
tangent of f(x)=x^2-5x+5,\at x=6	tangent\:f(x)=x^{2}-5x+5,\at\:x=6
taylor x^2cos(x),0.1	taylor\:x^{2}\cos(x),0.1
derivative of f(x)=-25x^2+150x-182	derivative\:f(x)=-25x^{2}+150x-182
integral of csc^3(2x)cot^3(2x)	\int\:\csc^{3}(2x)\cot^{3}(2x)dx
(tdy)/(dt)-3y=sqrt(t)	\frac{tdy}{dt}-3y=\sqrt{t}
(\partial)/(\partial z)(ze^{xyz})	\frac{\partial\:}{\partial\:z}(ze^{xyz})
limit as x approaches 0 of (x+1)/(x-1)	\lim\:_{x\to\:0}(\frac{x+1}{x-1})
derivative of x^{-4/5}	derivative\:x^{-\frac{4}{5}}
taylor 3/x	taylor\:\frac{3}{x}
integral of (x+1)/(x-1)	\int\:\frac{x+1}{x-1}dx
integral of ((-x^2-1))/((x^2-1))	\int\:\frac{(-x^{2}-1)}{(x^{2}-1)}dx
integral from 0 to 1 of 7e^{-4sqrt(x)}	\int\:_{0}^{1}7e^{-4\sqrt{x}}dx
limit as x approaches 3 of log_{4}(3x-5)	\lim\:_{x\to\:3}(\log_{4}(3x-5))
limit as x approaches-5+of 1/(x+5)	\lim\:_{x\to\:-5+}(\frac{1}{x+5})
integral of (9x)/((1-x^2)^3)	\int\:\frac{9x}{(1-x^{2})^{3}}dx
tangent of f(x)=4x^3sqrt(5x-1),\at x=1	tangent\:f(x)=4x^{3}\sqrt{5x-1},\at\:x=1
integral of (3x^2)/((1+x^3)^3)	\int\:\frac{3x^{2}}{(1+x^{3})^{3}}dx
(\partial)/(\partial x)(e^xy^2)	\frac{\partial\:}{\partial\:x}(e^{x}y^{2})
(dx)/(dt)= a/(xt)	\frac{dx}{dt}=\frac{a}{xt}
integral of-1/(2x+2)	\int\:-\frac{1}{2x+2}dx
limit as x approaches 2-of 6/(x-2)	\lim\:_{x\to\:2-}(\frac{6}{x-2})
derivative of f(x)=6x^4	derivative\:f(x)=6x^{4}

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