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Popular Calculus Problems

derivative of sqrt(5x-\sqrt{x)}	\frac{d}{dx}(\sqrt{5x-\sqrt{x}})
limit as x approaches-pi/2 of csc(x)	\lim\:_{x\to\:-\frac{π}{2}}(\csc(x))
derivative of ln(4x-x^2-3)	derivative\:\ln(4x-x^{2}-3)
integral of sin(2x)sin(cos(2x))	\int\:\sin(2x)\sin(\cos(2x))dx
(\partial)/(\partial x)(sin(3x+4y))	\frac{\partial\:}{\partial\:x}(\sin(3x+4y))
derivative of (4x+7)^2	derivative\:(4x+7)^{2}
integral of 1/(sqrt(2-x^2))	\int\:\frac{1}{\sqrt{2-x^{2}}}dx
derivative of (sqrt(x+4)/(sqrt(x-1)))	\frac{d}{dx}(\frac{\sqrt{x+4}}{\sqrt{x-1}})
derivative of ln(5x+2)	\frac{d}{dx}(\ln(5x+2))
derivative of sqrt(x+12)	derivative\:\sqrt{x+12}
(\partial)/(\partial x)(-(2y)/(3+2x))	\frac{\partial\:}{\partial\:x}(-\frac{2y}{3+2x})
integral of (-28)/(x^2sqrt(x^2+25))	\int\:\frac{-28}{x^{2}\sqrt{x^{2}+25}}dx
limit as x approaches 10 of 1/(x-10)	\lim\:_{x\to\:10}(\frac{1}{x-10})
sum from n=1 to infinity of (-3/2)^n	\sum\:_{n=1}^{\infty\:}(-\frac{3}{2})^{n}
integral from-1 to 0 of x-2	\int\:_{-1}^{0}x-2dx
integral of 1/(x(x+1)(x-2))	\int\:\frac{1}{x(x+1)(x-2)}dx
(dy)/(dx)= y/x+y^4	\frac{dy}{dx}=\frac{y}{x}+y^{4}
(x^2+3)(dy)/(dx)=xy	(x^{2}+3)\frac{dy}{dx}=xy
integral of (2x^3+4x^2-5)/(x+3)	\int\:\frac{2x^{3}+4x^{2}-5}{x+3}dx
derivative of (x^2/(x^2+1))	\frac{d}{dx}(\frac{x^{2}}{x^{2}+1})
derivative of 3x^4-4x^3-12x^2+5	\frac{d}{dx}(3x^{4}-4x^{3}-12x^{2}+5)
derivative of sin((pix/9))	\frac{d}{dx}(\sin(\frac{πx}{9}))
(\partial)/(\partial x)(xye^{-8y})	\frac{\partial\:}{\partial\:x}(xye^{-8y})
d/(dt)(4cos(t))	\frac{d}{dt}(4\cos(t))
derivative of (2x^2/(x-3))	\frac{d}{dx}(\frac{2x^{2}}{x-3})
integral of 1/(x^{1.4)}	\int\:\frac{1}{x^{1.4}}dx
integral of (y^2+26y+169)/((y^2+169)^2)	\int\:\frac{y^{2}+26y+169}{(y^{2}+169)^{2}}dy
integral of (cos(2x)+sin(2x))^2	\int\:(\cos(2x)+\sin(2x))^{2}dx
(ln(y))^7(dy)/(dx)=x^7y,y(1)=e^2	(\ln(y))^{7}\frac{dy}{dx}=x^{7}y,y(1)=e^{2}
simplify ((x^3-5x+186))/(x^2-x-42)	simplify\:\frac{(x^{3}-5x+186)}{x^{2}-x-42}
area sin(x),cos(x),(-pi)/(30), 25/12	area\:\sin(x),\cos(x),\frac{-π}{30},\frac{25}{12}
y^{''}+y^'+1.25y=0,y(0)=3,y^'(0)=1	y^{\prime\:\prime\:}+y^{\prime\:}+1.25y=0,y(0)=3,y^{\prime\:}(0)=1
integral of 23sec^{-2}(xta)n^3x	\int\:23\sec^{-2}(xta)n^{3}xdx
derivative of \sqrt[5]{x^2}-2/x	derivative\:\sqrt[5]{x^{2}}-\frac{2}{x}
integral of (x*e^x)/((x+1)^2)	\int\:\frac{x\cdot\:e^{x}}{(x+1)^{2}}dx
derivative of (x^4+1/(x^2+1))	\frac{d}{dx}(\frac{x^{4}+1}{x^{2}+1})
(\partial)/(\partial x)(y(e^{x^2-xy}))	\frac{\partial\:}{\partial\:x}(y(e^{x^{2}-xy}))
derivative of cos(e^{sqrt(tan(3x)}))	\frac{d}{dx}(\cos(e^{\sqrt{\tan(3x)}}))
integral of 6sin(6x)	\int\:6\sin(6x)dx
(\partial)/(\partial x)(e^6)	\frac{\partial\:}{\partial\:x}(e^{6})
derivative of (sqrt(x)+3x(x^{3/2}-x))	\frac{d}{dx}((\sqrt{x}+3x)(x^{\frac{3}{2}}-x))
integral of (x^2)/(sqrt(x^6+4))	\int\:\frac{x^{2}}{\sqrt{x^{6}+4}}dx
d/(dt)(-3sin(t))	\frac{d}{dt}(-3\sin(t))
derivative of f(x)=-5csc(x)+sec(x)	derivative\:f(x)=-5\csc(x)+\sec(x)
(\partial)/(\partial x)(4-sqrt(x^2+y^2))	\frac{\partial\:}{\partial\:x}(4-\sqrt{x^{2}+y^{2}})
integral of (8-sin(x))/(x^2)	\int\:\frac{8-\sin(x)}{x^{2}}dx
integral of sec^2(4x+9)	\int\:\sec^{2}(4x+9)dx
integral of 1/7 x^{-3/7}	\int\:\frac{1}{7}x^{-\frac{3}{7}}dx
integral of (sec^2(x)tan^4(x))	\int\:(\sec^{2}(x)\tan^{4}(x))dx
limit as x approaches 5 of 5x(5-x)	\lim\:_{x\to\:5}(5x(5-x))
derivative of (sin(10x)/(cos(10x)))	\frac{d}{dx}(\frac{\sin(10x)}{\cos(10x)})
y^'-y=2te^2t	y^{\prime\:}-y=2te^{2}t
derivative of cos(x+x^2sin(x))	\frac{d}{dx}(\cos(x)+x^{2}\sin(x))
(\partial)/(\partial y)(xe^{5y})	\frac{\partial\:}{\partial\:y}(xe^{5y})
derivative of (cos(x+2)^3(2x)^{-3x})	\frac{d}{dx}((\cos(x)+2)^{3}(2x)^{-3x})
sum from n=1 to infinity of ((-1)^nx^n)/(\sqrt[3]{n)}	\sum\:_{n=1}^{\infty\:}\frac{(-1)^{n}x^{n}}{\sqrt[3]{n}}
derivative of f(x)= 9/(x^3)	derivative\:f(x)=\frac{9}{x^{3}}
integral of sec^2(x)tan^3(x)	\int\:\sec^{2}(x)\tan^{3}(x)dx
derivative of ln(x-2x)	\frac{d}{dx}(\ln(x)-2x)
laplacetransform tsin(3t)+2tcos(t)	laplacetransform\:t\sin(3t)+2t\cos(t)
tangent of f(x)=(2x+1)/(x+2),\at x=1	tangent\:f(x)=\frac{2x+1}{x+2},\at\:x=1
(\partial)/(\partial x)(-(5x^3+5xy^2))	\frac{\partial\:}{\partial\:x}(-(5x^{3}+5xy^{2}))
(\partial)/(\partial h)(x^2h)	\frac{\partial\:}{\partial\:h}(x^{2}h)
maclaurin 1/(x+2)	maclaurin\:\frac{1}{x+2}
integral of (x^2-2)/(x^2+x)	\int\:\frac{x^{2}-2}{x^{2}+x}dx
integral of x^8e^x	\int\:x^{8}e^{x}dx
(x+2)(dy)/(dx)+y=ln(x),y(1)=20	(x+2)\frac{dy}{dx}+y=\ln(x),y(1)=20
area x,x^2,0,1	area\:x,x^{2},0,1
(\partial)/(\partial y)(x^2y+y^2z)	\frac{\partial\:}{\partial\:y}(x^{2}y+y^{2}z)
derivative of (x-14)/(sqrt(x)-\sqrt{14)}	derivative\:\frac{x-14}{\sqrt{x}-\sqrt{14}}
derivative of 1/(x(x+1))	\frac{d}{dx}(\frac{1}{x(x+1)})
limit as h approaches 0 of (4/(9+h)-4/9)/h	\lim\:_{h\to\:0}(\frac{\frac{4}{9+h}-\frac{4}{9}}{h})
integral of (3t+3)^{2.2}	\int\:(3t+3)^{2.2}dt
integral from 0 to 1 of sin(3pix)	\int\:_{0}^{1}\sin(3πx)dx
derivative of y=6x-11	derivative\:y=6x-11
integral of (5/x+sec^2(x))	\int\:(\frac{5}{x}+\sec^{2}(x))dx
derivative of-e^xsin(x+e^xcos(x))	\frac{d}{dx}(-e^{x}\sin(x)+e^{x}\cos(x))
limit as x approaches 2 of 3.5+5.6	\lim\:_{x\to\:2}(3.5+5.6)
limit as x approaches 2-of (2-\|x\|)/(2+x)	\lim\:_{x\to\:2-}(\frac{2-\left\|x\right\|}{2+x})
derivative of (4x+3)^5	derivative\:(4x+3)^{5}
y^{''}-3y^'-4y=6e^{2t}	y^{\prime\:\prime\:}-3y^{\prime\:}-4y=6e^{2t}
(\partial)/(\partial x)(e^{-(x^2+y^2+z^2)})	\frac{\partial\:}{\partial\:x}(e^{-(x^{2}+y^{2}+z^{2})})
limit as x approaches 0+of (3xe^{2x})/(sin(6x))	\lim\:_{x\to\:0+}(\frac{3xe^{2x}}{\sin(6x)})
y^'=0.0015y(400-y)	y^{\prime\:}=0.0015y(400-y)
limit as x approaches+0 of (1-2x)^{3/x}	\lim\:_{x\to\:+0}((1-2x)^{\frac{3}{x}})
derivative of bx^2(x-4)	\frac{d}{dx}(bx^{2}(x-4))
derivative of (x^2/(x^2+3))	\frac{d}{dx}(\frac{x^{2}}{x^{2}+3})
limit as x approaches 1 of 10x+1	\lim\:_{x\to\:1}(10x+1)
integral of x(x^2+2)^2	\int\:x(x^{2}+2)^{2}dx
inverse oflaplace 4(((1))/(s^2+16))	inverselaplace\:4(\frac{(1)}{s^{2}+16})
area y= 2/x ,y=7-x	area\:y=\frac{2}{x},y=7-x
integral of xsqrt(4-x^2)-x^2(sqrt(3))/3	\int\:x\sqrt{4-x^{2}}-x^{2}\frac{\sqrt{3}}{3}dx
(1+x)^2(dy)/(dx)=(1+y)^2	(1+x)^{2}\frac{dy}{dx}=(1+y)^{2}
derivative of xsqrt(9-x)	derivative\:x\sqrt{9-x}
integral of tan(-6x+3)	\int\:\tan(-6x+3)dx
integral of cos^3(x)sin^4(x)	\int\:\cos^{3}(x)\sin^{4}(x)dx
integral of 8sin^2(xco)s^3x	\int\:8\sin^{2}(xco)s^{3}xdx
f(x)= x/(4x-3ln(x))	f(x)=\frac{x}{4x-3\ln(x)}
derivative of e^{(x/2 ^2})	\frac{d}{dx}(e^{(\frac{x}{2})^{2}})
derivative of ((2x^2)/(x-2))	\frac{d}{dx}(\frac{(2x^{2})}{x-2})

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