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Popular Calculus Problems

tangent of y=sin(x),\at x=(5pi)/3	tangent\:y=\sin(x),\at\:x=\frac{5π}{3}
limit as x approaches 0 of (5^x-7^x)/x	\lim\:_{x\to\:0}(\frac{5^{x}-7^{x}}{x})
limit as x approaches 0 of (x^2-3)/x	\lim\:_{x\to\:0}(\frac{x^{2}-3}{x})
(dy)/(dx)(2)-4xy=8x	\frac{dy}{dx}(2)-4xy=8x
integral of 8^{3x+1}	\int\:8^{3x+1}dx
derivative of (x^2/(x^2-25))	\frac{d}{dx}(\frac{x^{2}}{x^{2}-25})
integral of ((1+y^2))/y	\int\:\frac{(1+y^{2})}{y}dy
roots x^2+ax+b	roots\:x^{2}+ax+b
derivative of 4cos(pix)	\frac{d}{dx}(4\cos(πx))
derivative of (693x^{5/2})/8	derivative\:\frac{693x^{\frac{5}{2}}}{8}
limit as (x,y) approaches (0,0) of xy	\lim\:_{(x,y)\to\:(0,0)}(xy)
(\partial)/(\partial x)(e^{-(x-vt)^2})	\frac{\partial\:}{\partial\:x}(e^{-(x-vt)^{2}})
(\partial)/(\partial x)(xcos(x)sin(x))	\frac{\partial\:}{\partial\:x}(x\cos(x)\sin(x))
derivative of f(x)=cos(x)sec(x)	derivative\:f(x)=\cos(x)\sec(x)
derivative of x^2-5	derivative\:x^{2}-5
derivative of (2x^{3x})	\frac{d}{dx}((2x)^{3x})
derivative of 5x-9	\frac{d}{dx}(5x-9)
y^{''}-5y^'+6y=sin(x)	y^{\prime\:\prime\:}-5y^{\prime\:}+6y=\sin(x)
integral of sec^2(3θ)	\int\:\sec^{2}(3θ)dθ
limit as x approaches 8-of x/(ln(9-x))	\lim\:_{x\to\:8-}(\frac{x}{\ln(9-x)})
derivative of arctan(x-1)	\frac{d}{dx}(\arctan(x-1))
y^'-((2x)/((1+x^2)))y=0	y^{\prime\:}-(\frac{2x}{(1+x^{2})})y=0
integral of ln(e^{u^2})	\int\:\ln(e^{u^{2}})du
3x-4ysqrt(x^2+1)(dy)/(dx)=0	3x-4y\sqrt{x^{2}+1}\frac{dy}{dx}=0
limit as x approaches 3 of x^2-4x	\lim\:_{x\to\:3}(x^{2}-4x)
integral of 4/(4x-1)	\int\:\frac{4}{4x-1}dx
derivative of ta{g}(t,xx)	\frac{d}{dx}(ta{g}(t,x)x)
derivative of 46*sin(x+10.7)	\frac{d}{dx}(46\cdot\:\sin(x)+10.7)
maclaurin arctan(x^2)	maclaurin\:\arctan(x^{2})
simplify 3e^x+4/(\sqrt[3]{x)}	simplify\:3e^{x}+\frac{4}{\sqrt[3]{x}}
integral from 1 to 2 of e^{-x}	\int\:_{1}^{2}e^{-x}dx
area 4x=y^2+12,3<= x<= 11	area\:4x=y^{2}+12,3\le\:x\le\:11
integral from 0 to pi/2 of \|7sin(x)-7cos(2x)\|	\int\:_{0}^{\frac{π}{2}}\left\|7\sin(x)-7\cos(2x)\right\|dx
tangent of y= 2/(x^2)	tangent\:y=\frac{2}{x^{2}}
integral from 6 to infinity of 1/(x^2+x)	\int\:_{6}^{\infty\:}\frac{1}{x^{2}+x}dx
(dy)/(dt)=2-y	\frac{dy}{dt}=2-y
(dy)/(dx)=x^4(32-x^5)^5	\frac{dy}{dx}=x^{4}(32-x^{5})^{5}
slope ofintercept (-1.6)(1.5)	slopeintercept\:(-1.6)(1.5)
taylor ln(x),x=1	taylor\:\ln(x),x=1
integral of (4x-2)/(x^4+x^2)	\int\:\frac{4x-2}{x^{4}+x^{2}}dx
derivative of y=ln(sqrt(x^2-4))	derivative\:y=\ln(\sqrt{x^{2}-4})
limit as x approaches 2 of 3-x^{1/(x^2)}	\lim\:_{x\to\:2}(3-x^{\frac{1}{x^{2}}})
derivative of (sqrt(x)dx)	\frac{d}{dx}((\sqrt{x})dx)
derivative of cos((1-e^{6x}/(1+e^{6x)}))	\frac{d}{dx}(\cos(\frac{1-e^{6x}}{1+e^{6x}}))
limit as x approaches infinity of 9.9	\lim\:_{x\to\:\infty\:}(9.9)
y^'=(x-y)/(x+y)	y^{\prime\:}=\frac{x-y}{x+y}
derivative of e^{2x}0.2	\frac{d}{dx}(e^{2x}0.2)
limit as x approaches 0 of xcot(x)	\lim\:_{x\to\:0}(x\cot(x))
10x-8ysqrt(x^2+1)y^'=0	10x-8y\sqrt{x^{2}+1}y^{\prime\:}=0
limit as x approaches 6 of 6(10)(-5)	\lim\:_{x\to\:6}(6(10)(-5))
tangent of y=0.0006x^{0.837}	tangent\:y=0.0006x^{0.837}
integral of 1/2 sec(x)tan(x)	\int\:\frac{1}{2}\sec(x)\tan(x)dx
derivative of f(x)=(100)/x	derivative\:f(x)=\frac{100}{x}
(dv)/(dt)+k/5 v+9.8=0	\frac{dv}{dt}+\frac{k}{5}v+9.8=0
integral of 5e^{0.3x}	\int\:5e^{0.3x}dx
(\partial)/(\partial x)(x/t)	\frac{\partial\:}{\partial\:x}(\frac{x}{t})
derivative of tan(5x^3)	\frac{d}{dx}(\tan(5x^{3}))
integral of e^{2x}ln(e^x)	\int\:e^{2x}\ln(e^{x})dx
tangent of y=x^2-8x,\at x=-8	tangent\:y=x^{2}-8x,\at\:x=-8
d/(d{y)}(e^{{x}{y}{z}})	\frac{d}{d{y}}(e^{{x}{y}{z}})
integral of (1/(2x^3))	\int\:(\frac{1}{2x^{3}})dx
integral of sin^3(xco)s^2x	\int\:\sin^{3}(xco)s^{2}xdx
integral of ((x^2-1))/(sqrt(x))	\int\:\frac{(x^{2}-1)}{\sqrt{x}}dx
integral of 2xsqrt(2x-3)	\int\:2x\sqrt{2x-3}dx
sum from n=1 to infinity of 7/(n(n+3))	\sum\:_{n=1}^{\infty\:}\frac{7}{n(n+3)}
derivative of e^xx-4e^x	derivative\:e^{x}x-4e^{x}
limit as x approaches 0 of (6^x-10^x)/x	\lim\:_{x\to\:0}(\frac{6^{x}-10^{x}}{x})
derivative of arccsc(4x)	\frac{d}{dx}(\arccsc(4x))
derivative of 1000x-x^2	\frac{d}{dx}(1000x-x^{2})
(x/2)^'	(\frac{x}{2})^{\prime\:}
integral of 5x^2sin(9x)	\int\:5x^{2}\sin(9x)dx
area 2sqrt(x),[1,2]	area\:2\sqrt{x},[1,2]
integral of 25	\int\:25
integral of 2/3 sec^2(x/3)	\int\:\frac{2}{3}\sec^{2}(\frac{x}{3})dx
integral of cos(3x)cos(5x)	\int\:\cos(3x)\cos(5x)dx
integral of (5x^3)/(sqrt(49-x^2))	\int\:\frac{5x^{3}}{\sqrt{49-x^{2}}}dx
integral of (-2x+4)/(x^4-2x^3+2x^2-2x+1)	\int\:\frac{-2x+4}{x^{4}-2x^{3}+2x^{2}-2x+1}dx
limit as x approaches 0 of sqrt(x+4)	\lim\:_{x\to\:0}(\sqrt{x+4})
limit as x approaches 0 of (e^{(-1)/x})/(x)	\lim\:_{x\to\:0}(\frac{e^{\frac{-1}{x}}}{x})
integral of z^2e^{-3z^3}	\int\:z^{2}e^{-3z^{3}}dz
integral from-5 to 5 of (sqrt(25-x^2))^2	\int\:_{-5}^{5}(\sqrt{25-x^{2}})^{2}dx
derivative of cos(5x*5)	\frac{d}{dx}(\cos(5x)\cdot\:5)
derivative of (2e^x)^2-(10e^x)	derivative\:(2e^{x})^{2}-(10e^{x})
integral of 1/(7x^3)	\int\:\frac{1}{7x^{3}}dx
derivative of (7x+sqrt(x^2+3)^6)	\frac{d}{dx}((7x+\sqrt{x^{2}+3})^{6})
parity (sin^5(e^{2x}))/(cos(7^{6x))}	parity\:\frac{\sin^{5}(e^{2x})}{\cos(7^{6x})}
integral of 2x-3x^2	\int\:2x-3x^{2}dx
d/(dt)(cos(7t))	\frac{d}{dt}(\cos(7t))
integral of (2x^2+4)/((x^2-2x+2)^2)	\int\:\frac{2x^{2}+4}{(x^{2}-2x+2)^{2}}dx
(\partial)/(\partial x)(x^4-yx^2+2y^3)	\frac{\partial\:}{\partial\:x}(x^{4}-yx^{2}+2y^{3})
(dy)/(dx)=3y+4	\frac{dy}{dx}=3y+4
integral of cos^4(7x+2)	\int\:\cos^{4}(7x+2)dx
tangent of y=6e^x+x,(0,6)	tangent\:y=6e^{x}+x,(0,6)
(\partial)/(\partial x)(e^z+1/x+xe^{-y})	\frac{\partial\:}{\partial\:x}(e^{z}+\frac{1}{x}+xe^{-y})
(dy}{dx}=\frac{4sqrt(y)ln(x))/x ,y(e)=1	\frac{dy}{dx}=\frac{4\sqrt{y}\ln(x)}{x},y(e)=1
limit as x approaches-2 of x^3+x-1	\lim\:_{x\to\:-2}(x^{3}+x-1)
derivative of 7/(x+1)	\frac{d}{dx}(\frac{7}{x+1})
derivative of x^2ln(x/4)	\frac{d}{dx}(x^{2}\ln(\frac{x}{4}))
derivative of 6x^4(x^2-7x)	\frac{d}{dx}(6x^{4}(x^{2}-7x))
integral from 0 to pi/2 of 17cos^5(x)	\int\:_{0}^{\frac{π}{2}}17\cos^{5}(x)dx

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