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Popular Calculus Problems

tangent of f(x)= 4/(x+1),\at x=6	tangent\:f(x)=\frac{4}{x+1},\at\:x=6
integral of 1/(2y-1)	\int\:\frac{1}{2y-1}dy
tangent of y=(x^3+2)(3x^2-4x+2),(1,3)	tangent\:y=(x^{3}+2)(3x^{2}-4x+2),(1,3)
tangent of x^2(2.4)	tangent\:x^{2}(2.4)
integral of 7x+5	\int\:7x+5dx
integral of ((2+x))/(sqrt(1-x^2))	\int\:\frac{(2+x)}{\sqrt{1-x^{2}}}dx
limit as x approaches 1 of \sqrt[x-1]{x}	\lim\:_{x\to\:1}(\sqrt[x-1]{x})
limit as x approaches 3+of 1/((x-3)^2)	\lim\:_{x\to\:3+}(\frac{1}{(x-3)^{2}})
integral of (sin(5x))/(1-cos(5x))	\int\:\frac{\sin(5x)}{1-\cos(5x)}dx
(dy)/((1+4y^2))=-x/((1+x^4))dx	\frac{dy}{(1+4y^{2})}=-\frac{x}{(1+x^{4})}dx
derivative of 6x^{3/2}	derivative\:6x^{\frac{3}{2}}
limit as x approaches infinity of 0.99^x	\lim\:_{x\to\:\infty\:}(0.99^{x})
d/(dt)(ate^t)	\frac{d}{dt}(ate^{t})
3xy^2y^'+3y^3=1	3xy^{2}y^{\prime\:}+3y^{3}=1
derivative of-2e^{-x}	\frac{d}{dx}(-2e^{-x})
derivative of sqrt(1+x^2+x^6)	\frac{d}{dx}(\sqrt{1+x^{2}+x^{6}})
y^{''}+y^'=3	y^{\prime\:\prime\:}+y^{\prime\:}=3
derivative of f(x)=x^2-x	derivative\:f(x)=x^{2}-x
d/(ds)(4^{-3}(2/(s^7)+3s)^4)	\frac{d}{ds}(4^{-3}(\frac{2}{s^{7}}+3s)^{4})
integral of x^3ln\|1+x\|	\int\:x^{3}\ln\left\|1+x\right\|dx
limit as x approaches-1 of (x-3)/(x+1)	\lim\:_{x\to\:-1}(\frac{x-3}{x+1})
derivative of f(x)=(x^3+2x^2+3x+4)/x	derivative\:f(x)=\frac{x^{3}+2x^{2}+3x+4}{x}
derivative of 9-x	\frac{d}{dx}(9-x)
derivative of 4pix^2	derivative\:4πx^{2}
sum from n=1 to infinity of 1/(n^2+2n)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{2}+2n}
inverse oflaplace 1/(s^2)-1/s+1/(s-2)	inverselaplace\:\frac{1}{s^{2}}-\frac{1}{s}+\frac{1}{s-2}
tangent of f(x)=(1-x)(x^2-3)^2	tangent\:f(x)=(1-x)(x^{2}-3)^{2}
sum from n=0 to infinity of 1^{2n}	\sum\:_{n=0}^{\infty\:}1^{2n}
(\partial)/(\partial z)(xcos(z))	\frac{\partial\:}{\partial\:z}(x\cos(z))
(dy)/(dx)=y(1/x-y)	\frac{dy}{dx}=y(\frac{1}{x}-y)
(\partial)/(\partial x)(3y-7)	\frac{\partial\:}{\partial\:x}(3y-7)
y^'=(t+y)^2-1,y(3)=4	y^{\prime\:}=(t+y)^{2}-1,y(3)=4
integral of sqrt(z)(z^2-1/(4z))	\int\:\sqrt{z}(z^{2}-\frac{1}{4z})dz
integral from 0 to 1 of xe^{x^2}	\int\:_{0}^{1}xe^{x^{2}}dx
integral of (ln^5(x))/x	\int\:\frac{\ln^{5}(x)}{x}dx
y^'=((2y+3)^2)/((4x+5)^2)	y^{\prime\:}=\frac{(2y+3)^{2}}{(4x+5)^{2}}
(\partial)/(\partial y)((x+2y)^2)	\frac{\partial\:}{\partial\:y}((x+2y)^{2})
derivative of (e^x-2/((1-e^{-x))^2})	\frac{d}{dx}(\frac{e^{x}-2}{(1-e^{-x})^{2}})
integral of ((5x^2))/(sqrt(1-5x^3))	\int\:\frac{(5x^{2})}{\sqrt{1-5x^{3}}}dx
limit as x approaches 0+of sin(pi/x)	\lim\:_{x\to\:0+}(\sin(\frac{π}{x}))
(\partial)/(\partial x)(y-x^2)	\frac{\partial\:}{\partial\:x}(y-x^{2})
2x^2y^'=y^'+6xe^{(-y)}	2x^{2}y^{\prime\:}=y^{\prime\:}+6xe^{(-y)}
integral of 2/3 t^{3/2}-2sin(t)+C	\int\:\frac{2}{3}t^{\frac{3}{2}}-2\sin(t)+Cdt
integral of (5x-x^2)	\int\:(5x-x^{2})dx
integral of x/(\sqrt[3]{x)}	\int\:\frac{x}{\sqrt[3]{x}}dx
integral of 10x^5e^x	\int\:10x^{5}e^{x}dx
7(dy)/(dx)=(e^ysin^2(x))/(ysec(x))	7\frac{dy}{dx}=\frac{e^{y}\sin^{2}(x)}{y\sec(x)}
f'(t)	f\prime\:(t)
limit as x approaches 0+of 1-x	\lim\:_{x\to\:0+}(1-x)
derivative of 3x^2cos(2x)	\frac{d}{dx}(3x^{2}\cos(2x))
integral of 1/2 (1+sin(θ))^2	\int\:\frac{1}{2}(1+\sin(θ))^{2}dθ
integral of excos(x)	\int\:ex\cos(x)dx
derivative of cos^9(t)	derivative\:\cos^{9}(t)
(\partial)/(\partial x)(2(y^2-x^2)ln(x+y))	\frac{\partial\:}{\partial\:x}(2(y^{2}-x^{2})\ln(x+y))
derivative of 3x^2-x^3	derivative\:3x^{2}-x^{3}
integral of 1/(4x^2+1)	\int\:\frac{1}{4x^{2}+1}dx
integral of 1/(y+sqrt(y))	\int\:\frac{1}{y+\sqrt{y}}dy
y^'=sin(x^2)	y^{\prime\:}=\sin(x^{2})
sum from n=0 to infinity of (n+4)/(3n+2)	\sum\:_{n=0}^{\infty\:}\frac{n+4}{3n+2}
integral of (z-3)^n	\int\:(z-3)^{n}dz
integral from-1 to 1 of (7x^3-2x^2+5x-4)	\int\:_{-1}^{1}(7x^{3}-2x^{2}+5x-4)dx
(dy)/(dx)=(2x+1)/(2y)	\frac{dy}{dx}=\frac{2x+1}{2y}
derivative of f(x)= 1/(sqrt(x+3))	derivative\:f(x)=\frac{1}{\sqrt{x+3}}
(sqrt(ln(x)))^'	(\sqrt{\ln(x)})^{\prime\:}
(dy)/(dx)=(-3y)	\frac{dy}{dx}=(-3y)
integral of sqrt(169-x^2)	\int\:\sqrt{169-x^{2}}dx
integral of (8x^3)/((x^4+1)^3)	\int\:\frac{8x^{3}}{(x^{4}+1)^{3}}dx
integral of (ln(sqrt(10x)))/x	\int\:\frac{\ln(\sqrt{10x})}{x}dx
y^{''}+12y^'+24y=4381e^{2x}cos(13x)	y^{\prime\:\prime\:}+12y^{\prime\:}+24y=4381e^{2x}\cos(13x)
inverse oflaplace (2s)/((s+3)^2)	inverselaplace\:\frac{2s}{(s+3)^{2}}
integral of e^{-st}sin(bt)	\int\:e^{-st}\sin(bt)dt
area y=sqrt(1-x^2),y=x^2-1	area\:y=\sqrt{1-x^{2}},y=x^{2}-1
x^3yy^'+x^2y^2=y^5	x^{3}yy^{\prime\:}+x^{2}y^{2}=y^{5}
(\partial)/(\partial y)(x^2e^{-x/y})	\frac{\partial\:}{\partial\:y}(x^{2}e^{-\frac{x}{y}})
integral of 13e^u	\int\:13e^{u}du
tangent of f(x)=x^2-3x+5,\at x=2	tangent\:f(x)=x^{2}-3x+5,\at\:x=2
y^'= y/x+sqrt(1+(y/x)^2)	y^{\prime\:}=\frac{y}{x}+\sqrt{1+(\frac{y}{x})^{2}}
integral of (x^2-12)/(x^3+4x)	\int\:\frac{x^{2}-12}{x^{3}+4x}dx
(\partial)/(\partial x)((2xy+3)e^{-xy})	\frac{\partial\:}{\partial\:x}((2xy+3)e^{-xy})
(\partial)/(\partial x)(arctan(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\arctan(x^{2}+y^{2}))
derivative of ((x^2-2e^x)/(x+3e^x))	\frac{d}{dx}(\frac{(x^{2}-2e^{x})}{x+3e^{x}})
integral of 1/(xsqrt(3x))	\int\:\frac{1}{x\sqrt{3x}}dx
derivative of 2ln(x^2+y^2)	\frac{d}{dx}(2\ln(x^{2}+y^{2}))
ty^'=(1-y^2)^{1/2}	ty^{\prime\:}=(1-y^{2})^{\frac{1}{2}}
integral of (e^{2x})/(x^2)	\int\:\frac{e^{2x}}{x^{2}}dx
taylor 1/(x-1),18	taylor\:\frac{1}{x-1},18
area sin(x),cos(x)	area\:\sin(x),\cos(x)
limit as x approaches 5-of sqrt(25-x^2)	\lim\:_{x\to\:5-}(\sqrt{25-x^{2}})
tangent of y=sqrt(x),(81,9)	tangent\:y=\sqrt{x},(81,9)
limit as x approaches 0 of sin(x)	\lim\:_{x\to\:0}(\sin(x))
integral of 1/(xy)	\int\:\frac{1}{xy}dx
(\partial)/(\partial r)(e^rcos(t))	\frac{\partial\:}{\partial\:r}(e^{r}\cos(t))
x^2((dy)/(dx))-xy+3y^2=0	x^{2}(\frac{dy}{dx})-xy+3y^{2}=0
integral from 0 to 2 of x^3sqrt(x^2+4)	\int\:_{0}^{2}x^{3}\sqrt{x^{2}+4}dx
(\partial)/(\partial y)(4y-3x^2)	\frac{\partial\:}{\partial\:y}(4y-3x^{2})
integral of (x^4)/((3+x^5)^2)	\int\:\frac{x^{4}}{(3+x^{5})^{2}}dx
integral of 1/(x*ln(x))	\int\:\frac{1}{x\cdot\:\ln(x)}dx
derivative of 4x+10	\frac{d}{dx}(4x+10)
limit as x approaches 1 of 3^{1/x}	\lim\:_{x\to\:1}(3^{\frac{1}{x}})
integral of (4x)/(sqrt(4x^2+5))	\int\:\frac{4x}{\sqrt{4x^{2}+5}}dx

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