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Popular Calculus Problems

(2x+3)^'	(2x+3)^{\prime\:}
derivative of In(x^3+x)	\frac{d}{dx}(In(x^{3}+x))
derivative of f(x)=2x^2+7x	derivative\:f(x)=2x^{2}+7x
derivative of x^4+7e^x	derivative\:x^{4}+7e^{x}
tangent of y=e^{3x},\at x= 1/3 ln(5)	tangent\:y=e^{3x},\at\:x=\frac{1}{3}\ln(5)
(\partial)/(\partial x)((5x)/(2y))	\frac{\partial\:}{\partial\:x}(\frac{5x}{2y})
integral from 0 to 1 of (e^{-0.2t})	\int\:_{0}^{1}(e^{-0.2t})dt
integral from 0 to 1 of sqrt(1+(\sqrt{2-x^2))^2}	\int\:_{0}^{1}\sqrt{1+(\sqrt{2-x^{2}})^{2}}dx
integral of arcsin(9x)	\int\:\arcsin(9x)dx
y^'+8y-6x=0	y^{\prime\:}+8y-6x=0
y^'= y/(y-x)	y^{\prime\:}=\frac{y}{y-x}
sum from n=1 to infinity of n^{-2.4}	\sum\:_{n=1}^{\infty\:}n^{-2.4}
integral of 1/(sqrt(1+y^2))	\int\:\frac{1}{\sqrt{1+y^{2}}}dy
integral from 1 to 4 of 8x-5	\int\:_{1}^{4}8x-5dx
(\partial)/(\partial x)(e^x)	\frac{\partial\:}{\partial\:x}(e^{x})
area X^2+X-12,X=0	area\:X^{2}+X-12,X=0
integral of-cos^{1/2}(3x)sin(3x)	\int\:-\cos^{\frac{1}{2}}(3x)\sin(3x)dx
(\partial)/(\partial y)(yx^{y-1})	\frac{\partial\:}{\partial\:y}(yx^{y-1})
y^{''}+6y^'+58y=0	y^{\prime\:\prime\:}+6y^{\prime\:}+58y=0
derivative of (-x^2/8)	\frac{d}{dx}(\frac{-x^{2}}{8})
integral of 1/((c^2+x^2))	\int\:\frac{1}{(c^{2}+x^{2})}dx
d/(dt)(2e^t)	\frac{d}{dt}(2e^{t})
integral of (11x^2)/((64+x^2)^2)	\int\:\frac{11x^{2}}{(64+x^{2})^{2}}dx
(\partial)/(\partial y)(-e^{-y/x})	\frac{\partial\:}{\partial\:y}(-e^{-\frac{y}{x}})
(dy)/(dx)+8y=9	\frac{dy}{dx}+8y=9
integral of xtan(2x)	\int\:x\tan(2x)dx
integral of (cos(7x))	\int\:(\cos(7x))dx
integral of tan^4(xse)c^4x	\int\:\tan^{4}(xse)c^{4}xdx
simplify t*e^{-t/2}	simplify\:t\cdot\:e^{-\frac{t}{2}}
derivative of 3x^2-6x+4	derivative\:3x^{2}-6x+4
d/(dt)(te^{at})	\frac{d}{dt}(te^{at})
(\partial)/(\partial y)(x^2y^3+2x^4y)	\frac{\partial\:}{\partial\:y}(x^{2}y^{3}+2x^{4}y)
derivative of sqrt(7-10x)	\frac{d}{dx}(\sqrt{7-10x})
integral of (sin(x))/(5+cos^2(x))	\int\:\frac{\sin(x)}{5+\cos^{2}(x)}dx
derivative of 1-\|1-x\|	\frac{d}{dx}(1-\left\|1-x\right\|)
integral of (x^4)/x	\int\:\frac{x^{4}}{x}dx
(x^2+2)^2y=(5x(y^2+1)^2)/((x^2+2)y^')-(x^4+4x^2+4)y	(x^{2}+2)^{2}y=\frac{5x(y^{2}+1)^{2}}{(x^{2}+2)y^{\prime\:}}-(x^{4}+4x^{2}+4)y
(dy)/(dx)= 1/(x^4+4x^2)	\frac{dy}{dx}=\frac{1}{x^{4}+4x^{2}}
limit as x approaches 2 of sin(1/(x-2))	\lim\:_{x\to\:2}(\sin(\frac{1}{x-2}))
limit as x approaches infinity of (4x^2+5x)/(sqrt(10+x^4))	\lim\:_{x\to\:\infty\:}(\frac{4x^{2}+5x}{\sqrt{10+x^{4}}})
3y^{''}-12y=0	3y^{\prime\:\prime\:}-12y=0
limit as x approaches 0+of 1/(x^3-2x^2)	\lim\:_{x\to\:0+}(\frac{1}{x^{3}-2x^{2}})
tangent of y=x^4+5x^2-x	tangent\:y=x^{4}+5x^{2}-x
integral of cos((npix)/2)	\int\:\cos(\frac{nπx}{2})dx
limit as x approaches 3+of (sqrt(3))/(sqrt(x)-\sqrt{3)}-2x	\lim\:_{x\to\:3+}(\frac{\sqrt{3}}{\sqrt{x}-\sqrt{3}}-2x)
derivative of ln(3x+5y)	\frac{d}{dx}(\ln(3x+5y))
derivative of 1/(4x-7)	\frac{d}{dx}(\frac{1}{4x-7})
limit as x approaches 0+of (1+tan(x))^{3/x}	\lim\:_{x\to\:0+}((1+\tan(x))^{\frac{3}{x}})
(\partial)/(\partial x)(56y^6x^6-42y^5x^5)	\frac{\partial\:}{\partial\:x}(56y^{6}x^{6}-42y^{5}x^{5})
derivative of arcsin(x+sqrt(1-x^2))	\frac{d}{dx}(\arcsin(x)+\sqrt{1-x^{2}})
derivative of f(x)=e^x-x^4	derivative\:f(x)=e^{x}-x^{4}
(\partial)/(\partial x)(-xe^x)	\frac{\partial\:}{\partial\:x}(-xe^{x})
sum from n=1 to infinity of ln(n/(2n+5))	\sum\:_{n=1}^{\infty\:}\ln(\frac{n}{2n+5})
integral of (x^2-x+6)/(x^3+3x)	\int\:\frac{x^{2}-x+6}{x^{3}+3x}dx
(\partial)/(\partial x)((x*y)/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{x\cdot\:y}{x+y})
derivative of ((x^2+1/(x^2-1))^8)	\frac{d}{dx}((\frac{x^{2}+1}{x^{2}-1})^{8})
(\partial)/(\partial x)(x^5+xy^7+4)	\frac{\partial\:}{\partial\:x}(x^{5}+xy^{7}+4)
limit as x approaches-3-of 4x^2-6x+3	\lim\:_{x\to\:-3-}(4x^{2}-6x+3)
limit as x approaches 3 of (ln(3-x))/(x-2)	\lim\:_{x\to\:3}(\frac{\ln(3-x)}{x-2})
derivative of (ln(x)^{ln(x)})	\frac{d}{dx}((\ln(x))^{\ln(x)})
limit as x approaches 7 of (x+4)/(x-7)	\lim\:_{x\to\:7}(\frac{x+4}{x-7})
derivative of f(2)=(x^2-4)/(x-2)	derivative\:f(2)=\frac{x^{2}-4}{x-2}
(\partial}{\partial t}(\frac{(3r+s))/t)	\frac{\partial\:}{\partial\:t}(\frac{(3r+s)}{t})
(d^2x)/(dt^2)=-kx	\frac{d^{2}x}{dt^{2}}=-kx
derivative of (8x^2-2x(5x+9))	\frac{d}{dx}((8x^{2}-2x)(5x+9))
y^{''}-4y^'+53y=0	y^{\prime\:\prime\:}-4y^{\prime\:}+53y=0
derivative of (x^5+1^6)	\frac{d}{dx}((x^{5}+1)^{6})
limit as x approaches 5 of x/(x+1)	\lim\:_{x\to\:5}(\frac{x}{x+1})
derivative of Inbx^4	derivative\:Inbx^{4}
integral of 5e^x-3cosh(x)	\int\:5e^{x}-3\cosh(x)dx
integral of-(2x)/(x^2+1)	\int\:-\frac{2x}{x^{2}+1}dx
integral of-x^3+5x^2-4x	\int\:-x^{3}+5x^{2}-4xdx
derivative of ((sqrt(x)/3+1)^{3/2})	\frac{d}{dx}((\frac{\sqrt{x}}{3}+1)^{\frac{3}{2}})
limit as x approaches infinity of (\sqrt[3]{8x^9+x^6+2})/(4x^3+x^2-1)	\lim\:_{x\to\:\infty\:}(\frac{\sqrt[3]{8x^{9}+x^{6}+2}}{4x^{3}+x^{2}-1})
integral of cos(x)(6+4sin^2(x))	\int\:\cos(x)(6+4\sin^{2}(x))dx
(\partial)/(\partial x)(9-3x^2-y^2)	\frac{\partial\:}{\partial\:x}(9-3x^{2}-y^{2})
limit as x approaches 2 of sqrt(3-x^2)	\lim\:_{x\to\:2}(\sqrt{3-x^{2}})
sum from n=0 to infinity of 3	\sum\:_{n=0}^{\infty\:}3
y^'=ysin(2x)	y^{\prime\:}=y\sin(2x)
integral of (5x-1)(3x^3+2)	\int\:(5x-1)(3x^{3}+2)dx
(\partial)/(\partial y)(x(x+y))	\frac{\partial\:}{\partial\:y}(x(x+y))
limit as x approaches infinity of x(arctan(x)-pi/2)	\lim\:_{x\to\:\infty\:}(x(\arctan(x)-\frac{π}{2}))
derivative of f(x)=(7x^6+8x^3)^4	derivative\:f(x)=(7x^{6}+8x^{3})^{4}
4y^{''}-4y^'-3y=0,y(0)=1,y^'(0)=5	4y^{\prime\:\prime\:}-4y^{\prime\:}-3y=0,y(0)=1,y^{\prime\:}(0)=5
limit as x approaches 0+of (cot(x))^{sin(x)}	\lim\:_{x\to\:0+}((\cot(x))^{\sin(x)})
(dy)/(dt)+2(t+1)y^2=0	\frac{dy}{dt}+2(t+1)y^{2}=0
integral of 15sin^3(x)cos^2(x)	\int\:15\sin^{3}(x)\cos^{2}(x)dx
x^2(dy)/(dx)-2xy=3y^4	x^{2}\frac{dy}{dx}-2xy=3y^{4}
integral of sqrt(5/x)	\int\:\sqrt{\frac{5}{x}}dx
derivative of e^{(-x^{1/2}+1/5 x^{-3/5}})	\frac{d}{dx}(e^{(-x^{\frac{1}{2}}+\frac{1}{5}x^{-\frac{3}{5}})})
integral of 1/((x^2+100)^2)	\int\:\frac{1}{(x^{2}+100)^{2}}dx
d/(d{y)}(-9sin(3{x}+{y}{z}))	\frac{d}{d{y}}(-9\sin(3{x}+{y}{z}))
limit as x approaches 0 of (cos^2(x))/x	\lim\:_{x\to\:0}(\frac{\cos^{2}(x)}{x})
(\partial ^2)/(\partial x\partial y)(ln(4+x^2y^2))	\frac{\partial\:^{2}}{\partial\:x\partial\:y}(\ln(4+x^{2}y^{2}))
integral of 1/(x(ln(x)+ln^2(x)))	\int\:\frac{1}{x(\ln(x)+\ln^{2}(x))}dx
limit as x approaches 2 of 7	\lim\:_{x\to\:2}(7)
derivative of (2x-3)^4(x^2+x+1)^5	derivative\:(2x-3)^{4}(x^{2}+x+1)^{5}
d/(dt)(Ate^t)	\frac{d}{dt}(Ate^{t})
sum from n=1 to infinity of n/(1-7n)	\sum\:_{n=1}^{\infty\:}\frac{n}{1-7n}
derivative of (-6x/(sqrt(2x-1)))	\frac{d}{dx}(\frac{-6x}{\sqrt{2x-1}})

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