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Popular Calculus Problems

derivative of-cos(x^2)sin(x)+e^{-x-2}	derivative\:-\cos(x^{2})\sin(x)+e^{-x-2}
(\partial)/(\partial x)(e^{2x+5y})	\frac{\partial\:}{\partial\:x}(e^{2x+5y})
derivative of cos(x-pi/4)	\frac{d}{dx}(\cos(x-\frac{π}{4}))
derivative of y=4x^2-2x+(-9)	derivative\:y=4x^{2}-2x+(-9)
d/(du)(sqrt(uv))	\frac{d}{du}(\sqrt{uv})
integral of 7x^{3/4}	\int\:7x^{\frac{3}{4}}dx
(dy)/(dx)=2sec^2(x)(y+3)	\frac{dy}{dx}=2\sec^{2}(x)(y+3)
derivative of (x^2+2x-2/(x^2-2x+2))	\frac{d}{dx}(\frac{x^{2}+2x-2}{x^{2}-2x+2})
integral of 1/(x^2sqrt(324-x^2))	\int\:\frac{1}{x^{2}\sqrt{324-x^{2}}}dx
integral of cos(9x)cos(3x)	\int\:\cos(9x)\cos(3x)dx
integral of 7xsec(x)tan(x)	\int\:7x\sec(x)\tan(x)dx
integral of 1/((576+x^2)^{3/2)}	\int\:\frac{1}{(576+x^{2})^{\frac{3}{2}}}dx
integral of 2acos(θ/2)	\int\:2a\cos(\frac{θ}{2})dθ
derivative of 1/2 x+sqrt(2)	\frac{d}{dx}(\frac{1}{2}x+\sqrt{2})
derivative of (1+cos^2(x))^6	derivative\:(1+\cos^{2}(x))^{6}
limit as t approaches pi of-2sin(-t/2)	\lim\:_{t\to\:π}(-2\sin(-\frac{t}{2}))
integral from 0 to infinity of af(x)	\int\:_{0}^{\infty\:}af(x)dx
limit as x approaches 2+of ln\|x-2\|	\lim\:_{x\to\:2+}(\ln\left\|x-2\right\|)
derivative of f(x)=7x-3x^2	derivative\:f(x)=7x-3x^{2}
integral of 1/(x^2-49)	\int\:\frac{1}{x^{2}-49}dx
inverse oflaplace 1/((s^3+s^2+s))	inverselaplace\:\frac{1}{(s^{3}+s^{2}+s)}
derivative of 7tan(x-7x)	\frac{d}{dx}(7\tan(x)-7x)
integral of (15)/(sqrt(4-5x))	\int\:\frac{15}{\sqrt{4-5x}}dx
limit as x approaches 0 of ((4tan(x)))/x	\lim\:_{x\to\:0}(\frac{(4\tan(x))}{x})
limit as x approaches+2 of (2x-1)^2-x^2	\lim\:_{x\to\:+2}((2x-1)^{2}-x^{2})
derivative of ln(e^{9x})	\frac{d}{dx}(\ln(e^{9x}))
xe^{x^2}dx+(y^5-1)dy=0,y(0)=0	xe^{x^{2}}dx+(y^{5}-1)dy=0,y(0)=0
integral of x^2\sqrt[3]{1-x}	\int\:x^{2}\sqrt[3]{1-x}dx
(d^2)/(dx^2)(2sec(x))	\frac{d^{2}}{dx^{2}}(2\sec(x))
(\partial)/(\partial x)(A+B(x^2+y^2))	\frac{\partial\:}{\partial\:x}(A+B(x^{2}+y^{2}))
limit as x approaches 1 of-2x+5	\lim\:_{x\to\:1}(-2x+5)
derivative of 2(x-1^{3/2})	\frac{d}{dx}(2(x-1)^{\frac{3}{2}})
(x^5+y^5)dx+5xy^4dy=0	(x^{5}+y^{5})dx+5xy^{4}dy=0
integral of (sqrt(x)sec(sqrt(x)))/(3x)	\int\:\frac{\sqrt{x}\sec(\sqrt{x})}{3x}dx
limit as x approaches 0 of 3x^3-2x^2+5	\lim\:_{x\to\:0}(3x^{3}-2x^{2}+5)
(\partial)/(\partial x)(cos(y))	\frac{\partial\:}{\partial\:x}(\cos(y))
(\partial)/(\partial y)(2ye^x-ln(z))	\frac{\partial\:}{\partial\:y}(2ye^{x}-\ln(z))
integral from 0 to 6 of f(x)	\int\:_{0}^{6}f(x)dx
derivative of sqrt(x^2+2x+8)	\frac{d}{dx}(\sqrt{x^{2}+2x+8})
(\partial)/(\partial x)(x^2-2xy+3y^2+2x-2y)	\frac{\partial\:}{\partial\:x}(x^{2}-2xy+3y^{2}+2x-2y)
derivative of f(x)=(2)(e^{3sqrt(x)})	derivative\:f(x)=(2)(e^{3\sqrt{x}})
derivative of-\|x\|	\frac{d}{dx}(-\left\|x\right\|)
derivative of (3x+1)^2	derivative\:(3x+1)^{2}
integral of sin(5x)sin(x)	\int\:\sin(5x)\sin(x)dx
integral of (4cos(x)+3x^2+2sin(x))	\int\:(4\cos(x)+3x^{2}+2\sin(x))dx
4y^{''}-12y^'+9y=0	4y^{\prime\:\prime\:}-12y^{\prime\:}+9y=0
area y=\sqrt[3]{2x},y= 1/8 x^2,(0,6)	area\:y=\sqrt[3]{2x},y=\frac{1}{8}x^{2},(0,6)
integral of e^{t/(RC)}	\int\:e^{\frac{t}{RC}}dt
integral of 9sqrt(x^7)	\int\:9\sqrt{x^{7}}dx
sum from n=2 to infinity of ((-1^n))/n	\sum\:_{n=2}^{\infty\:}\frac{(-1^{n})}{n}
derivative of f(x)=sqrt((x^26^x)^9)	derivative\:f(x)=\sqrt{(x^{2}6^{x})^{9}}
d/(dt)(3.5sin(5t))	\frac{d}{dt}(3.5\sin(5t))
(1/(x^3))^'	(\frac{1}{x^{3}})^{\prime\:}
derivative of y=(3x)^{5x}	derivative\:y=(3x)^{5x}
area y=9x,y= 3/4 x,y=70-x^2	area\:y=9x,y=\frac{3}{4}x,y=70-x^{2}
derivative of f(x)=(x+1)^{2/3}(2x^2-1)^3	derivative\:f(x)=(x+1)^{\frac{2}{3}}(2x^{2}-1)^{3}
maclaurin (1+x)^{1/4}	maclaurin\:(1+x)^{\frac{1}{4}}
derivative of \sqrt[3]{1+2x}	\frac{d}{dx}(\sqrt[3]{1+2x})
integral of (9sin(x))	\int\:(9\sin(x))dx
integral of e^xcos(y)	\int\:e^{x}\cos(y)dx
integral of 3x^2e^{8x^3}	\int\:3x^{2}e^{8x^{3}}dx
integral of (36)/(1-cos(9x))	\int\:\frac{36}{1-\cos(9x)}dx
integral from 1 to infinity of 5/(x^2)	\int\:_{1}^{\infty\:}\frac{5}{x^{2}}dx
taylor e^{2x+2}	taylor\:e^{2x+2}
limit as x approaches infinity of 0.7^x	\lim\:_{x\to\:\infty\:}(0.7^{x})
(dy)/(dx)+tan(x)y-cos(x)=0	\frac{dy}{dx}+\tan(x)y-\cos(x)=0
integral of 6x^2-8x	\int\:6x^{2}-8xdx
integral of 8-x	\int\:8-xdx
(dx)/(dt)+x/(25)=0.16	\frac{dx}{dt}+\frac{x}{25}=0.16
derivative of 3x^2-x^2y+y^4	\frac{d}{dx}(3x^{2}-x^{2}y+y^{4})
integral of (x+7)/(x^2+4x+8)	\int\:\frac{x+7}{x^{2}+4x+8}dx
6y^'-3y=2e^{-2x},y(0)=10	6y^{\prime\:}-3y=2e^{-2x},y(0)=10
taylor ln(1+2x),1	taylor\:\ln(1+2x),1
integral of cos^3(x/3)	\int\:\cos^{3}(\frac{x}{3})dx
area y=sqrt(x+2),y= 1/(x+1),x=0,x=2	area\:y=\sqrt{x+2},y=\frac{1}{x+1},x=0,x=2
(dy)/(dt)=y^{1.01}	\frac{dy}{dt}=y^{1.01}
integral of (ln(x))/(x^{1.2)}	\int\:\frac{\ln(x)}{x^{1.2}}dx
limit as x approaches-1 of 2x+2	\lim\:_{x\to\:-1}(2x+2)
integral of sin(x)*ln(cos(x))	\int\:\sin(x)\cdot\:\ln(\cos(x))dx
integral of 1/(\sqrt[3]{u)}	\int\:\frac{1}{\sqrt[3]{u}}du
derivative of f(x)=(2x)/((x^3-8)^2)	derivative\:f(x)=\frac{2x}{(x^{3}-8)^{2}}
taylor cos(x^4)	taylor\:\cos(x^{4})
(-sin(3x)*3)^'	(-\sin(3x)\cdot\:3)^{\prime\:}
limit as x approaches infinity of ((e^{2x}))/(x^2)	\lim\:_{x\to\:\infty\:}(\frac{(e^{2x})}{x^{2}})
(dy)/(dx)= x/y+y/x	\frac{dy}{dx}=\frac{x}{y}+\frac{y}{x}
(\partial)/(\partial x)((x^2+2y^2+3z^2)e^{-(x^2+y^2+z^2)})	\frac{\partial\:}{\partial\:x}((x^{2}+2y^{2}+3z^{2})e^{-(x^{2}+y^{2}+z^{2})})
integral of e^{(x^2)/2}x^3	\int\:e^{\frac{x^{2}}{2}}x^{3}dx
derivative of y=(2x+3)/(sqrt(x))	derivative\:y=\frac{2x+3}{\sqrt{x}}
limit as t approaches 6 of (8t-5)(t-7)	\lim\:_{t\to\:6}((8t-5)(t-7))
integral from 2 to 4 of tcos(t)	\int\:_{2}^{4}t\cos(t)dt
derivative of-2(2x^2cos(x^2+sin(x^2)))	\frac{d}{dx}(-2(2x^{2}\cos(x^{2})+\sin(x^{2})))
limit as x approaches 1 of (x^7-x)/(x-1)	\lim\:_{x\to\:1}(\frac{x^{7}-x}{x-1})
tangent of f(x)=4+x-2x^2-3x^3,\at x=2	tangent\:f(x)=4+x-2x^{2}-3x^{3},\at\:x=2
limit as x approaches 1 of 2/(x^3-1)	\lim\:_{x\to\:1}(\frac{2}{x^{3}-1})
derivative of sin(x^{cos(x}))	\frac{d}{dx}(\sin(x^{\cos(x)}))
y^'=3+e^{-2t}	y^{\prime\:}=3+e^{-2t}
laplacetransform t^2sin(4t)	laplacetransform\:t^{2}\sin(4t)
(dy)/(dt)+e^ty=12e^t	\frac{dy}{dt}+e^{t}y=12e^{t}
derivative of x/7+7/x	derivative\:\frac{x}{7}+\frac{7}{x}
inverse oflaplace F(s)=(s+9)/(s^2-2s-3)	inverselaplace\:F(s)=\frac{s+9}{s^{2}-2s-3}

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