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Popular Calculus Problems

derivative of x/(1-ln(x-4))	derivative\:\frac{x}{1-\ln(x-4)}
derivative of f(x)=2x^2-3	derivative\:f(x)=2x^{2}-3
derivative of x-sin(x)	derivative\:x-\sin(x)
(\partial}{\partial x}(sin(\frac{2y)/x))	\frac{\partial\:}{\partial\:x}(\sin(\frac{2y}{x}))
derivative of 6/((1+x^4))	\frac{d}{dx}(\frac{6}{(1+x)^{4}})
derivative of (6x^3-2/(x^2-4))	\frac{d}{dx}(\frac{6x^{3}-2}{x^{2}-4})
tangent of f(x)=x^2+x	tangent\:f(x)=x^{2}+x
integral of sec(5x)tan(5x)	\int\:\sec(5x)\tan(5x)dx
derivative of sec(1/(sqrt(x)))	\frac{d}{dx}(\sec(\frac{1}{\sqrt{x}}))
integral of 1/((x^2+9)^{5/2)}	\int\:\frac{1}{(x^{2}+9)^{\frac{5}{2}}}dx
limit as x approaches 1 of-1	\lim\:_{x\to\:1}(-1)
integral of (32r^7)/(sqrt(2-r^8))	\int\:\frac{32r^{7}dr}{\sqrt{2-r^{8}}}dx
derivative of x/(2x+5)	\frac{d}{dx}(\frac{x}{2x+5})
derivative of (1+sqrt(x)^3)	\frac{d}{dx}((1+\sqrt{x})^{3})
integral from 1 to 3 of (x^2+7)/(4x-x^2)	\int\:_{1}^{3}\frac{x^{2}+7}{4x-x^{2}}dx
(\partial)/(\partial x)(2xye^{-x^2-y^2})	\frac{\partial\:}{\partial\:x}(2xye^{-x^{2}-y^{2}})
derivative of 6sec(xtan(x))	\frac{d}{dx}(6\sec(x)\tan(x))
integral from 0 to infinity of e^{x/3}	\int\:_{0}^{\infty\:}e^{\frac{x}{3}}dx
x^2(dy)/(dx)+4xy-y^3=0	x^{2}\frac{dy}{dx}+4xy-y^{3}=0
integral from 0 to 1 of 2pi(x)(8-7x-x^2)	\int\:_{0}^{1}2π(x)(8-7x-x^{2})dx
integral from 0 to 1 of 5/(x^5)	\int\:_{0}^{1}\frac{5}{x^{5}}dx
derivative of (24/(x^2+12))	\frac{d}{dx}(\frac{24}{x^{2}+12})
limit as x approaches 1 of e^x-1	\lim\:_{x\to\:1}(e^{x}-1)
(dy)/(dt)= y/2+4e^{t/2}	\frac{dy}{dt}=\frac{y}{2}+4e^{\frac{t}{2}}
y^{''''}-y^{''}+y=0	y^{\prime\:\prime\:\prime\:\prime\:}-y^{\prime\:\prime\:}+y=0
2y^{''}-7y^'-15y=0,y(0)=2,y^'(0)=1	2y^{\prime\:\prime\:}-7y^{\prime\:}-15y=0,y(0)=2,y^{\prime\:}(0)=1
derivative of f(x)=x^3+6x^2+xdf(x)	derivative\:f(x)=x^{3}+6x^{2}+xdf(x)
derivative of sqrt(3x+4y)	\frac{d}{dx}(\sqrt{3x+4y})
integral of (30)/((1-x^2)^{3/2)}	\int\:\frac{30}{(1-x^{2})^{\frac{3}{2}}}dx
integral of 3xln(x^8)	\int\:3x\ln(x^{8})dx
derivative of (x-7)(2x-9)	derivative\:(x-7)(2x-9)
(\partial)/(\partial x)(x^2cos(x)y)	\frac{\partial\:}{\partial\:x}(x^{2}\cos(x)y)
integral of e^{-θ}cos(2θ)	\int\:e^{-θ}\cos(2θ)dθ
integral of (2x-9)e^{2x}	\int\:(2x-9)e^{2x}dx
derivative of-(3y/(3x+2y))	\frac{d}{dx}(-\frac{3y}{3x+2y})
derivative of 1/((3-x^2))	\frac{d}{dx}(\frac{1}{(3-x)^{2}})
laplacetransform cos(k*t)	laplacetransform\:\cos(k\cdot\:t)
(dy)/(dx)=y^{1/3},y(1)=0	\frac{dy}{dx}=y^{\frac{1}{3}},y(1)=0
((x^2+1)dy)/(dx)=-y^2-1	\frac{(x^{2}+1)dy}{dx}=-y^{2}-1
derivative of f(3)=10+12x-3x^2-x^3	derivative\:f(3)=10+12x-3x^{2}-x^{3}
derivative of y=6x-x^2	derivative\:y=6x-x^{2}
derivative of ln((\|x\|)/(sqrt(1+x^2)))	derivative\:\ln(\frac{\left\|x\right\|}{\sqrt{1+x^{2}}})
(\partial)/(\partial x)(4x^2+5xy^2)	\frac{\partial\:}{\partial\:x}(4x^{2}+5xy^{2})
integral of (1-2x)	\int\:(1-2x)dx
area f(x)=2x-8,[7,10]	area\:f(x)=2x-8,[7,10]
d/(dt)(-2asin(2t)+2bcos(2t))	\frac{d}{dt}(-2a\sin(2t)+2b\cos(2t))
sum from n=0 to infinity of 3n	\sum\:_{n=0}^{\infty\:}3n
taylor x-1-0.5sin(x)	taylor\:x-1-0.5\sin(x)
integral from sqrt(8) to-1 of x^2-8	\int\:_{\sqrt{8}}^{-1}x^{2}-8dx
y^'-(6y)/x =(y^4)/(x^{12)}	y^{\prime\:}-\frac{6y}{x}=\frac{y^{4}}{x^{12}}
2xyy^'=x^2+y^2	2xyy^{\prime\:}=x^{2}+y^{2}
integral of (1-2x^5)/x	\int\:\frac{1-2x^{5}}{x}dx
integral from 0 to 1 of (1-x^2)^{3/2}	\int\:_{0}^{1}(1-x^{2})^{\frac{3}{2}}dx
integral of (15)/(x^2+1)	\int\:\frac{15}{x^{2}+1}dx
(\partial)/(\partial x)(\sqrt[3]{x})	\frac{\partial\:}{\partial\:x}(\sqrt[3]{x})
derivative of e^{17x}	derivative\:e^{17x}
f(x)=sqrt(x)ln(x)	f(x)=\sqrt{x}\ln(x)
derivative of xe^{2x^2-4x}	\frac{d}{dx}(xe^{2x^{2}-4x})
tangent of y=x^3-2x+2,(4,58)	tangent\:y=x^{3}-2x+2,(4,58)
derivative of-1/((1-x)^2)	derivative\:-\frac{1}{(1-x)^{2}}
taylor 2/x ,1	taylor\:\frac{2}{x},1
(dy)/(dx)=4x(x-1)	\frac{dy}{dx}=4x(x-1)
integral from 0 to 1 of (xsqrt(1-x^2))	\int\:_{0}^{1}(x\sqrt{1-x^{2}})dx
derivative of f(x)=e^{2x-5}+4	derivative\:f(x)=e^{2x-5}+4
y^'=(y^2+3xsqrt(x^2+y^2))/(xy)	y^{\prime\:}=\frac{y^{2}+3x\sqrt{x^{2}+y^{2}}}{xy}
integral of x(x+1)^6	\int\:x(x+1)^{6}dx
integral of (x/(sqrt(x^2-2)))	\int\:(\frac{x}{\sqrt{x^{2}-2}})dx
integral of 6/(\sqrt[4]{7-4x)}	\int\:\frac{6}{\sqrt[4]{7-4x}}dx
laplacetransform 10cos(8t)+14sin(8t)	laplacetransform\:10\cos(8t)+14\sin(8t)
limit as x approaches 1 of 2x^{3/2}-3x^2	\lim\:_{x\to\:1}(2x^{\frac{3}{2}}-3x^{2})
derivative of 7sqrt(x^2+8x)	\frac{d}{dx}(7\sqrt{x^{2}+8x})
tangent of f(x)=3x^2+2x,\at p(-1,5)	tangent\:f(x)=3x^{2}+2x,\at\:p(-1,5)
derivative of cos(4x*4)	\frac{d}{dx}(\cos(4x)\cdot\:4)
sum from n=1 to infinity of (2n^2)/(n!)	\sum\:_{n=1}^{\infty\:}\frac{2n^{2}}{n!}
(\partial)/(\partial x)(sin(pi(5x-3y)))	\frac{\partial\:}{\partial\:x}(\sin(π(5x-3y)))
integral of sqrt(1+(4/(3x^{1/3)))^2}	\int\:\sqrt{1+(\frac{4}{3x^{\frac{1}{3}}})^{2}}dx
derivative of y=(f(x))/(x^2+2)	derivative\:y=\frac{f(x)}{x^{2}+2}
(\partial)/(\partial L)(L^{1/4})	\frac{\partial\:}{\partial\:L}(L^{\frac{1}{4}})
integral of (2-8x)/(sqrt(81-4x^2))	\int\:\frac{2-8x}{\sqrt{81-4x^{2}}}dx
(dx)/(dt)=c_{1}x-c_{2}x^2	\frac{dx}{dt}=c_{1}x-c_{2}x^{2}
integral from-1 to 2 of 3/(x^2)	\int\:_{-1}^{2}\frac{3}{x^{2}}dx
sum from n=0 to infinity of 5^n	\sum\:_{n=0}^{\infty\:}5^{n}
(arctan(y))^'	(\arctan(y))^{\prime\:}
integral of 27x^2+C	\int\:27x^{2}+Cdx
integral of \sqrt[3]{x^2-5x+1}(2x-5)	\int\:\sqrt[3]{x^{2}-5x+1}(2x-5)dx
integral from 0 to infinity of 3sin^2(x)	\int\:_{0}^{\infty\:}3\sin^{2}(x)dx
area y=4x,y=4x^2	area\:y=4x,y=4x^{2}
limit as x approaches 0 of x/(-14x^4+5x)	\lim\:_{x\to\:0}(\frac{x}{-14x^{4}+5x})
integral of (y^2)/(1+y^3)	\int\:\frac{y^{2}}{1+y^{3}}dy
tangent of y=9e^xcos(x),(0,9)	tangent\:y=9e^{x}\cos(x),(0,9)
derivative of (x+sin(x)^5)	\frac{d}{dx}((x+\sin(x))^{5})
tangent of 3tan(x),\at x= pi/3	tangent\:3\tan(x),\at\:x=\frac{π}{3}
d/(dθ)(2sin(θ)+2cos(θ))	\frac{d}{dθ}(2\sin(θ)+2\cos(θ))
slope of (9.5)(21.1)	slope\:(9.5)(21.1)
(d^2)/(dx^2)(5(x^2+3x)^3)	\frac{d^{2}}{dx^{2}}(5(x^{2}+3x)^{3})
derivative of (-sin(x)/(sqrt(2)))	\frac{d}{dx}(\frac{-\sin(x)}{\sqrt{2}})
integral of (2x-1)/(sqrt(1-x^2))	\int\:\frac{2x-1}{\sqrt{1-x^{2}}}dx
limit as x approaches+4+of 2x-7	\lim\:_{x\to\:+4+}(2x-7)
derivative of 2/(x^{1/2})	\frac{d}{dx}(\frac{2}{x^{\frac{1}{2}}})
integral of 1/(4e^{-8x)+e^{8x}}	\int\:\frac{1}{4e^{-8x}+e^{8x}}dx

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