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Popular Calculus Problems

(\partial)/(\partial x)(6xy-6x)	\frac{\partial\:}{\partial\:x}(6xy-6x)
limit as x approaches 7 of 4x	\lim\:_{x\to\:7}(4x)
derivative of-x^2-4x+4	\frac{d}{dx}(-x^{2}-4x+4)
x^2y^{''}-3xy^'-2y=0	x^{2}y^{\prime\:\prime\:}-3xy^{\prime\:}-2y=0
limit as x approaches-pi/3 of-sec(x)	\lim\:_{x\to\:-\frac{π}{3}}(-\sec(x))
integral of (x(x+1)^3)	\int\:(x(x+1)^{3})dx
derivative of (3x^4-x+1)(-x^5+4)	derivative\:(3x^{4}-x+1)(-x^{5}+4)
integral of (x-1)/(x^2(x+1))	\int\:\frac{x-1}{x^{2}(x+1)}dx
f(t)=sin(2t)	f(t)=\sin(2t)
integral of-1/((t+1)^2)	\int\:-\frac{1}{(t+1)^{2}}dt
derivative of x^2+4x((36.5/(x^2)))	\frac{d}{dx}(x^{2}+4x(\frac{36.5}{x^{2}}))
tangent of f(x)=x+sqrt(x),(4,6)	tangent\:f(x)=x+\sqrt{x},(4,6)
integral of 1/((144-x^2)^{3/2)}	\int\:\frac{1}{(144-x^{2})^{\frac{3}{2}}}dx
derivative of e^{-x-y}	\frac{d}{dx}(e^{-x-y})
integral of y^2cos(x)+cos(y)	\int\:y^{2}\cos(x)+\cos(y)dx
integral of (x^3)/((x-1)(x^2+3))	\int\:\frac{x^{3}}{(x-1)(x^{2}+3)}dx
(\partial)/(\partial x)(xcos(θ))	\frac{\partial\:}{\partial\:x}(x\cos(θ))
derivative of f(x)=5e^xsqrt(x)	derivative\:f(x)=5e^{x}\sqrt{x}
integral of (sqrt(36-25x^2))/x	\int\:\frac{\sqrt{36-25x^{2}}}{x}dx
limit as x approaches-6 of (-8x)/(x+6)	\lim\:_{x\to\:-6}(\frac{-8x}{x+6})
(\partial)/(\partial y)(-e^xsin(y))	\frac{\partial\:}{\partial\:y}(-e^{x}\sin(y))
y^'+y(1-2x)=-(x^2)/2 y	y^{\prime\:}+y(1-2x)=-\frac{x^{2}}{2}y
derivative of y=e^{1/(x^2)}+1/(e^{x^2)}	derivative\:y=e^{\frac{1}{x^{2}}}+\frac{1}{e^{x^{2}}}
derivative of (2x/(sqrt(x+20)))	\frac{d}{dx}(\frac{2x}{\sqrt{x+20}})
ydy=-xdx	ydy=-xdx
(\partial)/(\partial x)(x^2-0.1cos(6x))	\frac{\partial\:}{\partial\:x}(x^{2}-0.1\cdot\:\cos(6\cdot\:x))
(dy)/(dx)=3+e^{-3x+y+4}	\frac{dy}{dx}=3+e^{-3x+y+4}
integral of (x^2+1)sqrt(x-2)	\int\:(x^{2}+1)\sqrt{x-2}dx
integral from 0 to 1 of 1/(t^2+1)	\int\:_{0}^{1}\frac{1}{t^{2}+1}dt
(2x+2y-3)/(-x-y-1)=(dy)/(dx)	\frac{2x+2y-3}{-x-y-1}=\frac{dy}{dx}
x^2y^{''}-2xy^'+2y=x^3e^x	x^{2}y^{\prime\:\prime\:}-2xy^{\prime\:}+2y=x^{3}e^{x}
integral of (5x)/(9x^2-4)	\int\:\frac{5x}{9x^{2}-4}dx
sum from n=0 to infinity of e^{(-n)/2}	\sum\:_{n=0}^{\infty\:}e^{\frac{-n}{2}}
(x+y)dx+(x)dy=0	(x+y)dx+(x)dy=0
integral of (2-sin(t/4))^2cos(t/4)	\int\:(2-\sin(\frac{t}{4}))^{2}\cos(\frac{t}{4})dt
(dy)/(dx)=(cos(2x))	\frac{dy}{dx}=(\cos(2x))
y^{''}+y^'-2y=0,y(0)=-5,y^'(0)=-1	y^{\prime\:\prime\:}+y^{\prime\:}-2y=0,y(0)=-5,y^{\prime\:}(0)=-1
integral of (2ysin(x)+e^{2z})	\int\:(2y\sin(x)+e^{2z})dy
y^{''}+12y^'+45y=0	y^{\prime\:\prime\:}+12y^{\prime\:}+45y=0
integral from 1 to 2 of (9x^3+4x^2-2)/x	\int\:_{1}^{2}\frac{9x^{3}+4x^{2}-2}{x}dx
integral of (sec(x))/(tan^2(x))	\int\:\frac{\sec(x)}{\tan^{2}(x)}dx
sum from n=1 to infinity of 7(3)^n	\sum\:_{n=1}^{\infty\:}7(3)^{n}
integral of x/(x)	\int\:\frac{x}{d+x}dx
integral of (2x-3)^3	\int\:(2x-3)^{3}dx
integral of cos(7x)	\int\:\cos(7x)dx
integral of sin^4(3θ)	\int\:\sin^{4}(3θ)dθ
integral of 4/(xln(x))	\int\:\frac{4}{x\ln(x)}dx
integral from 0 to 5 of (4x-x^2)	\int\:_{0}^{5}(4x-x^{2})dx
derivative of \sqrt[3]{x}+4sqrt(x^3)	derivative\:\sqrt[3]{x}+4\sqrt{x^{3}}
integral of 6sin^2(x)	\int\:6\sin^{2}(x)dx
derivative of 11sec^2(x)	\frac{d}{dx}(11\sec^{2}(x))
derivative of cy^{-5}	derivative\:cy^{-5}
(\partial)/(\partial y)(6xzsin(y))	\frac{\partial\:}{\partial\:y}(6xz\sin(y))
derivative of (2x/8)	\frac{d}{dx}(\frac{2x}{8})
derivative of-(200/(x^2))	\frac{d}{dx}(-\frac{200}{x^{2}})
integral of sqrt(1-x^2)	\int\:\sqrt{1-x^{2}}dx
integral of (2x-5)^2	\int\:(2x-5)^{2}dx
(\partial)/(\partial x)(4x^2y-4x+3y^3)	\frac{\partial\:}{\partial\:x}(4x^{2}y-4x+3y^{3})
integral from 1 to e^4 of x^2ln(x)	\int\:_{1}^{e^{4}}x^{2}\ln(x)dx
ye^{2x}dx=(4+e^{2x})dy	ye^{2x}dx=(4+e^{2x})dy
xy^2y^'=y^3-x^3,y(1)=2	xy^{2}y^{\prime\:}=y^{3}-x^{3},y(1)=2
sum from n=1 to infinity of n(4/5)^n	\sum\:_{n=1}^{\infty\:}n(\frac{4}{5})^{n}
integral of-9xe^{-3x}	\int\:-9xe^{-3x}dx
(x^2+y^2)dx+3xydy=0	(x^{2}+y^{2})dx+3xydy=0
limit as x approaches-1 of (\sqrt[3]{7-x^3}-\sqrt[3]{3+x^2})/(x+1)	\lim\:_{x\to\:-1}(\frac{\sqrt[3]{7-x^{3}}-\sqrt[3]{3+x^{2}}}{x+1})
derivative of 210^x	\frac{d}{dx}(210^{x})
integral of e^{3x+e^{3x}}	\int\:e^{3x+e^{3x}}dx
integral of sqrt(5-y)	\int\:\sqrt{5-y}dy
derivative of 1/(2sqrt(r))+1/(4r^{3/4)}	derivative\:\frac{1}{2\sqrt{r}}+\frac{1}{4r^{\frac{3}{4}}}
inverse oflaplace x	inverselaplace\:x
derivative of 1/((2+x^2))	\frac{d}{dx}(\frac{1}{(2+x)^{2}})
derivative of arctan(x/2)	derivative\:\arctan(\frac{x}{2})
limit as x approaches infinity of (ln(x))^{1/(x^2)}	\lim\:_{x\to\:\infty\:}((\ln(x))^{\frac{1}{x^{2}}})
integral of x^4in(x)	\int\:x^{4}in(x)dx
y^'+a^2y=0	y^{\prime\:}+a^{2}y=0
(\partial)/(\partial x)(-2sin(2x)-2xe^{5y})	\frac{\partial\:}{\partial\:x}(-2\sin(2x)-2xe^{5y})
f(s)= s/(s^2+1)	f(s)=\frac{s}{s^{2}+1}
integral from-1 to 0 of 3/(3x-2)	\int\:_{-1}^{0}\frac{3}{3x-2}dx
derivative of f(x)=-3x^2+6x+4	derivative\:f(x)=-3x^{2}+6x+4
derivative of (1+2x^{ln(x)})	\frac{d}{dx}((1+2x)^{\ln(x)})
limit as h approaches 0 of 0/h	\lim\:_{h\to\:0}(\frac{0}{h})
inverse oflaplace s/((s^2+4^2)^2)	inverselaplace\:\frac{s}{(s^{2}+4^{2})^{2}}
integral of sin(nx+x)	\int\:\sin(nx+x)dx
(\partial)/(\partial x)(8e^{x^6y})	\frac{\partial\:}{\partial\:x}(8e^{x^{6}y})
integral of x^5sqrt(x^6+8)	\int\:x^{5}\sqrt{x^{6}+8}dx
integral of (ln(x))/(x^{18)}	\int\:\frac{\ln(x)}{x^{18}}dx
integral of (x^2+2)	\int\:(x^{2}+2)dx
(\partial)/(\partial y)(-cos(xy))	\frac{\partial\:}{\partial\:y}(-\cos(xy))
limit as x approaches 0 of (e^x-1)ln(x)	\lim\:_{x\to\:0}((e^{x}-1)\ln(x))
(dy)/(dx)=(xy)^{1/3}	\frac{dy}{dx}=(xy)^{\frac{1}{3}}
area 1,cos^2(x),[0,pi]	area\:1,\cos^{2}(x),[0,π]
derivative of f(5)=(4x^2+7x+7)/(sqrt(x))	derivative\:f(5)=\frac{4x^{2}+7x+7}{\sqrt{x}}
derivative of ((x+1^3)/((x-1)^2))	\frac{d}{dx}(\frac{(x+1)^{3}}{(x-1)^{2}})
integral of sin^3(2θ)sqrt(cos(2θ))	\int\:\sin^{3}(2θ)\sqrt{\cos(2θ)}dθ
integral of (4sin(x))	\int\:(4\sin(x))dx
(\partial)/(\partial x)(2sin^2(x))	\frac{\partial\:}{\partial\:x}(2\sin^{2}(x))
derivative of (4x^2+4x+4)/(sqrt(x))	derivative\:\frac{4x^{2}+4x+4}{\sqrt{x}}
derivative of (x^3*e^x-ln(x)/(sec(x)))	\frac{d}{dx}(\frac{x^{3}\cdot\:e^{x}-\ln(x)}{\sec(x)})
slope of xy-5y^2=8	slope\:xy-5y^{2}=8
integral of sin^5(t)cos^6(t)	\int\:\sin^{5}(t)\cos^{6}(t)dt

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