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Popular Calculus Problems

derivative of 2e^{-x}cos(x)	\frac{d}{dx}(2e^{-x}\cos(x))
derivative of f(x)=(2x^2+2x+4)/(sqrt(x))	derivative\:f(x)=\frac{2x^{2}+2x+4}{\sqrt{x}}
integral of e^{x^2-1}	\int\:e^{x^{2}-1}dx
derivative of 1/(s^2+16)	derivative\:\frac{1}{s^{2}+16}
tangent of f(x)=sqrt(4x+33),(4,7)	tangent\:f(x)=\sqrt{4x+33},(4,7)
(\partial)/(\partial y)(sin(xy^2))	\frac{\partial\:}{\partial\:y}(\sin(xy^{2}))
integral from-1 to 1 of x^4-2x^2+1	\int\:_{-1}^{1}x^{4}-2x^{2}+1dx
integral of y/(y^2-1)	\int\:\frac{y}{y^{2}-1}dy
parity sin(cos(tan(x)))	parity\:\sin(\cos(\tan(x)))
(\partial)/(\partial y)(x/(y+2z))	\frac{\partial\:}{\partial\:y}(\frac{x}{y+2z})
sum from n=1 to infinity of (-0.75)^n	\sum\:_{n=1}^{\infty\:}(-0.75)^{n}
integral of x(x-5)	\int\:x(x-5)dx
area y=2x^2ln(x),y=8ln(x)	area\:y=2x^{2}\ln(x),y=8\ln(x)
integral of (48)/((t+1)^4)-3	\int\:\frac{48}{(t+1)^{4}}-3dt
(dy}{dx}=\frac{x^7-8y)/x	\frac{dy}{dx}=\frac{x^{7}-8y}{x}
integral from 0 to 1 of e^{2sqrt(x)}	\int\:_{0}^{1}e^{2\sqrt{x}}dx
2xydx-(1+x^2)dy=0	2xydx-(1+x^{2})dy=0
integral of (x^2)/(sqrt(4-25x^2))	\int\:\frac{x^{2}}{\sqrt{4-25x^{2}}}dx
integral of 1/(x(sqrt(x-1)))	\int\:\frac{1}{x(\sqrt{x-1})}dx
y^'-(cos(x))y=(e^{sin(x)})/(sqrt(1-x^2))	y^{\prime\:}-(\cos(x))y=\frac{e^{\sin(x)}}{\sqrt{1-x^{2}}}
derivative of 3sin(x+8cos(x))	\frac{d}{dx}(3\sin(x)+8\cos(x))
limit as x approaches 0+of sin(x)*ln(3x)	\lim\:_{x\to\:0+}(\sin(x)\cdot\:\ln(3x))
integral from 0 to 2 of 6x^2	\int\:_{0}^{2}6x^{2}dx
integral from-1 to 1 of xsqrt(1-x^2)	\int\:_{-1}^{1}x\sqrt{1-x^{2}}dx
integral of sin(24x)cos(15x)	\int\:\sin(24x)\cos(15x)dx
derivative of 8/(sqrt(x-2))	\frac{d}{dx}(\frac{8}{\sqrt{x-2}})
integral of x^2*e^{x^3+4}	\int\:x^{2}\cdot\:e^{x^{3}+4}dx
derivative of r(θ,xcos(θ))	\frac{d}{dx}(r(θ,x)\cos(θ))
derivative of y=4arcsin(5)x^5	derivative\:y=4\arcsin(5)x^{5}
taylor (1+x)^{-1}	taylor\:(1+x)^{-1}
tangent of y=-3x^3-2x^2-x+3,(-1,5)	tangent\:y=-3x^{3}-2x^{2}-x+3,(-1,5)
derivative of-1/(x^2)	derivative\:-\frac{1}{x^{2}}
(dy)/(dx)=20x	\frac{dy}{dx}=20x
integral of x/((x^2+1))	\int\:\frac{x}{(x^{2}+1)}dx
(\partial)/(\partial x)(6x^{4y})	\frac{\partial\:}{\partial\:x}(6x^{4y})
integral of x^3sqrt(1-x)	\int\:x^{3}\sqrt{1-x}dx
derivative of 4-(25/(6x^{1/6)})	\frac{d}{dx}(4-\frac{25}{6x^{\frac{1}{6}}})
derivative of ln(3x^2+7)	\frac{d}{dx}(\ln(3x^{2}+7))
tangent of f(x)=x-1/x ,\at x=1	tangent\:f(x)=x-\frac{1}{x},\at\:x=1
y^{''}+81y=4tan(9x)	y^{\prime\:\prime\:}+81y=4\tan(9x)
limit as x approaches 4 of x/4+1	\lim\:_{x\to\:4}(\frac{x}{4}+1)
integral of 6.5sqrt(x)	\int\:6.5\sqrt{x}dx
inverse oflaplace ((10s+3))/(s^2+4s+29)	inverselaplace\:\frac{(10s+3)}{s^{2}+4s+29}
limit as x approaches 0+of x^{-5}	\lim\:_{x\to\:0+}(x^{-5})
(\partial)/(\partial x)(8x)	\frac{\partial\:}{\partial\:x}(8x)
integral of 4pix^2	\int\:4πx^{2}dx
normal of y=8xe^x,(0,0)	normal\:y=8xe^{x},(0,0)
derivative of f(x)=(x^2-2e^x)/(x+3e^x)	derivative\:f(x)=\frac{x^{2}-2e^{x}}{x+3e^{x}}
integral of 1/3 sec^2(8x)	\int\:\frac{1}{3}\sec^{2}(8x)dx
integral of sin(2t)cos(t)	\int\:\sin(2t)\cos(t)dt
derivative of y=(5x-4)(2x^3-x^2+1)	derivative\:y=(5x-4)(2x^{3}-x^{2}+1)
y^{''}+3y^'+0=5	y^{\prime\:\prime\:}+3y^{\prime\:}+0=5
integral from 0 to 1/3 of 2/(1+9x^2)	\int\:_{0}^{\frac{1}{3}}\frac{2}{1+9x^{2}}dx
tangent of f(x)=x^3-16x+5,\at x=4	tangent\:f(x)=x^{3}-16x+5,\at\:x=4
integral from 0 to 2 of 1/(x^2-5x+4)	\int\:_{0}^{2}\frac{1}{x^{2}-5x+4}dx
derivative of 2/(1+e^{-x})	\frac{d}{dx}(\frac{2}{1+e^{-x}})
sum from n=0 to infinity of 3(-1/2)^n	\sum\:_{n=0}^{\infty\:}3(-\frac{1}{2})^{n}
limit as x approaches 2 of 4/((x-2)^5)	\lim\:_{x\to\:2}(\frac{4}{(x-2)^{5}})
tangent of f(x)=x+e^x-1/x ,\at x=1	tangent\:f(x)=x+e^{x}-\frac{1}{x},\at\:x=1
integral of-(2x)/(x^4-1)	\int\:-\frac{2x}{x^{4}-1}dx
limit as x approaches pi/3 of cos(x)	\lim\:_{x\to\:\frac{π}{3}}(\cos(x))
limit as x approaches 1 of (-x+1)/(x-1)	\lim\:_{x\to\:1}(\frac{-x+1}{x-1})
integral of 12x^2(2x^3+3)^7	\int\:12x^{2}(2x^{3}+3)^{7}dx
integral of (x+5)/(sqrt(x))	\int\:\frac{x+5}{\sqrt{x}}dx
integral of (26x^3-52x^2+8)/(x^2-2x)	\int\:\frac{26x^{3}-52x^{2}+8}{x^{2}-2x}dx
integral of cot(16x)	\int\:\cot(16x)dx
limit as x approaches 0-of 5/(x^3)	\lim\:_{x\to\:0-}(\frac{5}{x^{3}})
derivative of x^{18}	derivative\:x^{18}
derivative of tan(2xcot(2x))	\frac{d}{dx}(\tan(2x)\cot(2x))
laplacetransform 35	laplacetransform\:35
derivative of f(x)=5e^x+8/(\sqrt[3]{x)}	derivative\:f(x)=5e^{x}+\frac{8}{\sqrt[3]{x}}
(\partial)/(\partial y)(x^2y-xy^2)	\frac{\partial\:}{\partial\:y}(x^{2}y-xy^{2})
derivative of y=(tan(x)-1)/(sec(x))	derivative\:y=\frac{\tan(x)-1}{\sec(x)}
y^{'''}-9y^{''}+y^'-9y=0	y^{\prime\:\prime\:\prime\:}-9y^{\prime\:\prime\:}+y^{\prime\:}-9y=0
y^{''}-4y^'+3y=(2x+1)e^{-x}	y^{\prime\:\prime\:}-4y^{\prime\:}+3y=(2x+1)e^{-x}
limit as x approaches 0-of 0/(x^2\|x\|)	\lim\:_{x\to\:0-}(\frac{0}{x^{2}\left\|x\right\|})
derivative of sqrt((e^x/3))	\frac{d}{dx}(\sqrt{\frac{e^{x}}{3}})
integral from 4y^2+4z^2 to 4 of x	\int\:_{4y^{2}+4z^{2}}^{4}xdx
derivative of (x^2-1(x^3+3x))	\frac{d}{dx}((x^{2}-1)(x^{3}+3x))
(y^2)^'	(y^{2})^{\prime\:}
derivative of f(x)=x^2-sqrt(x)+2	derivative\:f(x)=x^{2}-\sqrt{x}+2
(dy)/(dx)y=x^{-12}	\frac{dy}{dx}y=x^{-12}
(\partial)/(\partial y)(x^2y+e^{xy})	\frac{\partial\:}{\partial\:y}(x^{2}y+e^{xy})
derivative of x+6	\frac{d}{dx}(x+6)
integral of 3cos^5(x)sin^4(x)	\int\:3\cos^{5}(x)\sin^{4}(x)dx
integral of (4x)/(sqrt(2x^2+1))	\int\:\frac{4x}{\sqrt{2x^{2}+1}}dx
limit as x approaches infinity of 1/x+2	\lim\:_{x\to\:\infty\:}(\frac{1}{x}+2)
y^{''}+(a+b)y=0	y^{\prime\:\prime\:}+(a+b)y=0
integral of sin^9(x)	\int\:\sin^{9}(x)dx
integral of 6/(sqrt(x+6)+\sqrt{x)}	\int\:\frac{6}{\sqrt{x+6}+\sqrt{x}}dx
integral of g(x)	\int\:g(x)dx
sum from n=1 to infinity of arctan(12n)	\sum\:_{n=1}^{\infty\:}\arctan(12n)
integral of x(x+6)^{1/2}	\int\:x(x+6)^{\frac{1}{2}}dx
integral of 1/(5x+2)	\int\:\frac{1}{5x+2}dx
integral from 1 to sqrt(2 of)xe^{3x^2}	\int\:_{1}^{\sqrt{2}}xe^{3x^{2}}dx
(dy)/(dx)= y/x	\frac{dy}{dx}=\frac{y}{x}
(\partial)/(\partial y)((cy)/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{cy}{x^{2}+y^{2}})
(4+x)y^'=y^3	(4+x)y^{\prime\:}=y^{3}
limit as x approaches 2 of 1/(sqrt(x-1))	\lim\:_{x\to\:2}(\frac{1}{\sqrt{x-1}})
sum from i=1 to infinity of (i)*1/(6^i)	\sum\:_{i=1}^{\infty\:}(i)\cdot\:\frac{1}{6^{i}}

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