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Popular Calculus Problems

derivative of sin(2x+cos(3x))	\frac{d}{dx}(\sin(2x)+\cos(3x))
tangent of f(x)=pi^{3x+3},\at x=2	tangent\:f(x)=π^{3x+3},\at\:x=2
121y^{''}+88y^'+12y=0	121y^{\prime\:\prime\:}+88y^{\prime\:}+12y=0
derivative of sqrt(4+cot^2(x))	derivative\:\sqrt{4+\cot^{2}(x)}
derivative of sqrt(x+5)	derivative\:\sqrt{x+5}
integral from 0 to N of e^{-st}e^{5t}	\int\:_{0}^{N}e^{-st}e^{5t}dt
limit as x approaches 2 of-x+6	\lim\:_{x\to\:2}(-x+6)
limit as h approaches 0 of 2+h	\lim\:_{h\to\:0}(2+h)
integral of e^rr+e^r	\int\:e^{r}r+e^{r}dr
integral of cos^3(x)*sin(x)	\int\:\cos^{3}(x)\cdot\:\sin(x)dx
y^{''}-3y^'-4y=3e^{2x}	y^{\prime\:\prime\:}-3y^{\prime\:}-4y=3e^{2x}
integral from 2 to 3 of 3x	\int\:_{2}^{3}3xdx
integral from 0 to pi/4 of (tan(x))^2	\int\:_{0}^{\frac{π}{4}}(\tan(x))^{2}dx
derivative of-6x^3	\frac{d}{dx}(-6x^{3})
limit as x approaches-1 of 3f(x)-2h(x)	\lim\:_{x\to\:-1}(3f(x)-2h(x))
derivative of ln(sqrt((x+7)/(x-7)))	derivative\:\ln(\sqrt{\frac{x+7}{x-7}})
derivative of (2x+1e^{-x})	\frac{d}{dx}((2x+1)e^{-x})
sum from n=0 to infinity of 2/(n^2+2n)	\sum\:_{n=0}^{\infty\:}\frac{2}{n^{2}+2n}
integral of (x^2+3)/(x^3+2x)	\int\:\frac{x^{2}+3}{x^{3}+2x}dx
derivative of ln(3x^2-y^3-3)	\frac{d}{dx}(\ln(3x^{2}-y^{3}-3))
derivative of 3^{x^2cot(2x})	\frac{d}{dx}(3^{x^{2}\cot(2x)})
derivative of 8/(\sqrt[3]{x})	\frac{d}{dx}(\frac{8}{\sqrt[3]{x}})
derivative of (x+3)/(x-3)	derivative\:\frac{x+3}{x-3}
integral of 7e^{10x}	\int\:7e^{10x}dx
integral of 4cos(θ)	\int\:4\cos(θ)dθ
integral of (3x+1)\sqrt[3]{3x^2+2x}	\int\:(3x+1)\sqrt[3]{3x^{2}+2x}dx
integral of (x^3+x^2+x-2)/(x^3-x^2)	\int\:\frac{x^{3}+x^{2}+x-2}{x^{3}-x^{2}}dx
area 4-x^2, 1/4 x^3-2,1,2	area\:4-x^{2},\frac{1}{4}x^{3}-2,1,2
(dy)/(dx)=(8x^2)/(sqrt(9+x^3))	\frac{dy}{dx}=\frac{8x^{2}}{\sqrt{9+x^{3}}}
derivative of h^2+7h+40	derivative\:h^{2}+7h+40
y^'=xy^8	y^{\prime\:}=xy^{8}
integral from 0 to x of x	\int\:_{0}^{x}xdx
tangent of f(x)= 5/(2sqrt(5x+4)),\at x=9	tangent\:f(x)=\frac{5}{2\sqrt{5x+4}},\at\:x=9
(\partial)/(\partial x)(sin(pi(2x-4y)))	\frac{\partial\:}{\partial\:x}(\sin(π(2x-4y)))
(\partial)/(\partial x)(arcsin(x/y))	\frac{\partial\:}{\partial\:x}(\arcsin(\frac{x}{y}))
limit as x approaches 0 of-((1+x^2)^{cot(x)})	\lim\:_{x\to\:0}(-((1+x^{2})^{\cot(x)}))
d/(dt)(((sqrt(2)ty))/3)	\frac{d}{dt}(\frac{(\sqrt{2}ty)}{3})
area y=e^x,y=2e^{-x}+1,x=0	area\:y=e^{x},y=2e^{-x}+1,x=0
(\partial)/(\partial x)(-4sin(2x))	\frac{\partial\:}{\partial\:x}(-4\sin(2x))
implicit (dy)/(dx),x^3+y^3=36	implicit\:\frac{dy}{dx},x^{3}+y^{3}=36
slope of (0,1),(1,-3)	slope\:(0,1),(1,-3)
limit as x approaches-infinity of x-4	\lim\:_{x\to\:-\infty\:}(x-4)
inverse oflaplace 2/(s^3(s^2+9))	inverselaplace\:\frac{2}{s^{3}(s^{2}+9)}
integral of (1/(x^6))	\int\:(\frac{1}{x^{6}})dx
(\partial)/(\partial x)(0.1sqrt(x)*y)	\frac{\partial\:}{\partial\:x}(0.1\sqrt{x}\cdot\:y)
(dx)/(dt)+2tx=t	\frac{dx}{dt}+2tx=t
xy^'+2y=-2cos(x)	xy^{\prime\:}+2y=-2\cos(x)
limit as x approaches (5pi)/6 of (sin(x))/(cos(x))	\lim\:_{x\to\:\frac{5π}{6}}(\frac{\sin(x)}{\cos(x)})
slope of (2.1)(-14.7)	slope\:(2.1)(-14.7)
derivative of 640(1.06)^t	derivative\:640(1.06)^{t}
derivative of f(x)=2x^2-32	derivative\:f(x)=2x^{2}-32
laplacetransform f(t)=5+4*\delta(t)	laplacetransform\:f(t)=5+4\cdot\:\delta(t)
derivative of ln(1+sin(x))	\frac{d}{dx}(\ln(1+\sin(x)))
derivative of (f(x(6x))^2-2)	\frac{d}{dx}((f(x)(6x))^{2}-2)
limit as x approaches 0+of 2+ln(x)	\lim\:_{x\to\:0+}(2+\ln(x))
integral of (cos(3x))^3	\int\:(\cos(3x))^{3}dx
derivative of-e^{4x}	\frac{d}{dx}(-e^{4x})
(y^2+1)dx=(1+xy)dy	(y^{2}+1)dx=(1+xy)dy
derivative of sin(x)*tan(x)	derivative\:\sin(x)\cdot\:\tan(x)
integral of-8e^{-8x}	\int\:-8e^{-8x}dx
integral of 1/((9+x^2)^2)	\int\:\frac{1}{(9+x^{2})^{2}}dx
y(1+x^2)y^'-x(5+y^2)=0	y(1+x^{2})y^{\prime\:}-x(5+y^{2})=0
integral from 0 to 1 of 6e^{-2x}	\int\:_{0}^{1}6e^{-2x}dx
derivative of e^8	derivative\:e^{8}
laplacetransform 2((e^{2t}+e^{-2t})/2)sin(2t)	laplacetransform\:2(\frac{e^{2t}+e^{-2t}}{2})\sin(2t)
(\partial)/(\partial x)(z^2x^3)	\frac{\partial\:}{\partial\:x}(z^{2}x^{3})
derivative of f(x)=sqrt(x^2+3)	derivative\:f(x)=\sqrt{x^{2}+3}
integral of 2arctan(sqrt(x))	\int\:2\arctan(\sqrt{x})dx
area f(x)=x^5+4,g(x)=x+4	area\:f(x)=x^{5}+4,g(x)=x+4
tangent of f(x)=-1/(2sqrt(1-x)),\at x=-8	tangent\:f(x)=-\frac{1}{2\sqrt{1-x}},\at\:x=-8
integral of 1/(usqrt(7-u^2))	\int\:\frac{1}{u\sqrt{7-u^{2}}}du
f^'(x)=(8x^5-6x^9)/(x^4)	f^{\prime\:}(x)=\frac{8x^{5}-6x^{9}}{x^{4}}
derivative of ln(1+e^{2x})	\frac{d}{dx}(\ln(1+e^{2x}))
limit as x approaches-1 of (x^2-x)/x	\lim\:_{x\to\:-1}(\frac{x^{2}-x}{x})
integral from 2 to infinity of 1/(x^2-1)	\int\:_{2}^{\infty\:}\frac{1}{x^{2}-1}dx
(dy)/(dx)+y=y^2,y(0)=2	\frac{dy}{dx}+y=y^{2},y(0)=2
integral of sqrt(y/4)	\int\:\sqrt{\frac{y}{4}}dy
derivative of ((sqrt(x))/(7+x))	\frac{d}{dx}(\frac{(\sqrt{x})}{7+x})
(2xy+3x^2)dx+(x^2-1)dy=0	(2xy+3x^{2})dx+(x^{2}-1)dy=0
integral of pisin(8pix)	\int\:π\sin(8πx)dx
integral of (1/(13x))	\int\:(\frac{1}{13x})dx
integral from 0 to 2 of x^2e^{-5x}	\int\:_{0}^{2}x^{2}e^{-5x}dx
derivative of 2sin^2(3x+2cos^2(3x))	\frac{d}{dx}(2\sin^{2}(3x)+2\cos^{2}(3x))
(\partial)/(\partial y)(x^2-xy)	\frac{\partial\:}{\partial\:y}(x^{2}-xy)
integral from 0 to ln(5) of xe^x	\int\:_{0}^{\ln(5)}xe^{x}dx
laplacetransform e^tcos(2t)	laplacetransform\:e^{t}\cos(2t)
derivative of e^{0x}	\frac{d}{dx}(e^{0x})
f(x)=(pix)/2	f(x)=\frac{πx}{2}
derivative of 64x-(x^3/3)	\frac{d}{dx}(64x-\frac{x^{3}}{3})
derivative of ln(6x^2+3x)	\frac{d}{dx}(\ln(6x^{2}+3x))
limit as x approaches 1 of (x-2)^2	\lim\:_{x\to\:1}((x-2)^{2})
sum from n=1 to infinity of (1/2)^{n+1}	\sum\:_{n=1}^{\infty\:}(\frac{1}{2})^{n+1}
(\partial)/(\partial x)(ln(x^2+2x))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+2x))
(\partial)/(\partial x)(-3y^3+3x^2y^2-y)	\frac{\partial\:}{\partial\:x}(-3y^{3}+3x^{2}y^{2}-y)
y^'=24x^2e^{-y}	y^{\prime\:}=24x^{2}e^{-y}
integral of 4-3(1-x^2)^{-1}	\int\:4-3(1-x^{2})^{-1}dx
derivative of y-y=4	\frac{d}{dx}y-y=4
derivative of f(x)=(-2x)/(x^2+1)	derivative\:f(x)=\frac{-2x}{x^{2}+1}
integral of (5-50x)/(sqrt(4-25x^2))	\int\:\frac{5-50x}{\sqrt{4-25x^{2}}}dx
integral of 2^{sqrt(x)}	\int\:2^{\sqrt{x}}dx

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