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Popular Calculus Problems

derivative of csc^2(x-2)	\frac{d}{dx}(\csc^{2}(x-2))
(\partial)/(\partial x)(x^{0.4}y^{0.6})	\frac{\partial\:}{\partial\:x}(x^{0.4}y^{0.6})
derivative of sqrt(1+2e^{3x)}	\frac{d}{dx}(\sqrt{1+2e^{3x}})
integral of ((x+1))/(x^3+x^2-6x)	\int\:\frac{(x+1)}{x^{3}+x^{2}-6x}dx
integral from 3 to 4 of x/(x-3)	\int\:_{3}^{4}\frac{x}{x-3}dx
integral of ln((sqrt(x))/(1+sqrt(x)))	\int\:\ln(\frac{\sqrt{x}}{1+\sqrt{x}})dx
tangent of f(x)=5sqrt(x)	tangent\:f(x)=5\sqrt{x}
integral from 1 to 4 of sqrt(x)(1+x)	\int\:_{1}^{4}\sqrt{x}(1+x)dx
integral of (2u^2-1)/(u^3-u)	\int\:\frac{2u^{2}-1}{u^{3}-u}du
integral from 100 to 120 of 600	\int\:_{100}^{120}600dx
(d^2)/(dx^2)(\sqrt[9]{x})	\frac{d^{2}}{dx^{2}}(\sqrt[9]{x})
integral of (8x)/(sqrt(3-4x^2))	\int\:\frac{8x}{\sqrt{3-4x^{2}}}dx
integral from 1 to 4 of (3x^2+1)	\int\:_{1}^{4}(3x^{2}+1)dx
4x-(5ysqrt(x^2+1)dy)/(dx)=0,y(0)=-10	4x-\frac{5y\sqrt{x^{2}+1}dy}{dx}=0,y(0)=-10
f(x)=(x-4)/(x^2)	f(x)=\frac{x-4}{x^{2}}
integral of (sec^3(θ))/(tan(θ))	\int\:\frac{\sec^{3}(θ)}{\tan(θ)}dθ
derivative of f(x)=16cos(2x)	derivative\:f(x)=16\cos(2x)
(e^x+y)dx+(2+x+ye^y)dy=0,y(0)=1	(e^{x}+y)dx+(2+x+ye^{y})dy=0,y(0)=1
sum from n=0 to infinity of n(n+1)x^n	\sum\:_{n=0}^{\infty\:}n\cdot\:(n+1)\cdot\:x^{n}
integral of 1/(sqrt(16+6x-x^2))	\int\:\frac{1}{\sqrt{16+6x-x^{2}}}dx
(\partial}{\partial x}(\frac{y^4)/x)	\frac{\partial\:}{\partial\:x}(\frac{y^{4}}{x})
derivative of arcsin(x-y)	\frac{d}{dx}(\arcsin(x-y))
integral from-1 to 3 of 3x+1	\int\:_{-1}^{3}3x+1dx
tangent of y=x^2,\at x= 1/3	tangent\:y=x^{2},\at\:x=\frac{1}{3}
(\partial)/(\partial y)((5(y+2))/((x+2)^2))	\frac{\partial\:}{\partial\:y}(\frac{5(y+2)}{(x+2)^{2}})
(\partial)/(\partial x)(y^x-ln(x^4y+6x))	\frac{\partial\:}{\partial\:x}(y^{x}-\ln(x^{4}y+6x))
(\partial)/(\partial y)(2x^2-3y^2-2x)	\frac{\partial\:}{\partial\:y}(2x^{2}-3y^{2}-2x)
(\partial)/(\partial x)(sin(x)+cos(-6y))	\frac{\partial\:}{\partial\:x}(\sin(x)+\cos(-6y))
(\partial)/(\partial x)((5xy^2)/(x^2+y^4))	\frac{\partial\:}{\partial\:x}(\frac{5xy^{2}}{x^{2}+y^{4}})
inverse oflaplace (20)/(s*(s+10))	inverselaplace\:\frac{20}{s\cdot\:(s+10)}
limit as t approaches 7 of (sqrt((t-7)^3))/(t-7)	\lim\:_{t\to\:7}(\frac{\sqrt{(t-7)^{3}}}{t-7})
sum from n=0 to infinity of 1/(10n+1)	\sum\:_{n=0}^{\infty\:}\frac{1}{10n+1}
integral of (x^3-x)	\int\:(x^{3}-x)dx
sum from n=1 to infinity of 3(1/2)^{n-1}	\sum\:_{n=1}^{\infty\:}3(\frac{1}{2})^{n-1}
integral of (1+e^x)^2	\int\:(1+e^{x})^{2}dx
derivative of-5t(2t^7-1)^5	derivative\:-5t(2t^{7}-1)^{5}
limit as x approaches 3+of (ln(x))/(x-3)	\lim\:_{x\to\:3+}(\frac{\ln(x)}{x-3})
inverse oflaplace (s+2)/((s^2+4))	inverselaplace\:\frac{s+2}{(s^{2}+4)}
d/(dt)(1/3 t^3)	\frac{d}{dt}(\frac{1}{3}t^{3})
y^{''}+25y=te^{6t}	y^{\prime\:\prime\:}+25y=te^{6t}
derivative of e^{x+c}	\frac{d}{dx}(e^{x+c})
integral of 1/(x^2+t^2)	\int\:\frac{1}{x^{2}+t^{2}}dx
derivative of 1/3 tan^3(x-tan(x)+x)	\frac{d}{dx}(\frac{1}{3}\tan^{3}(x)-\tan(x)+x)
derivative of f(x)=(x+9)(x^2-9)	derivative\:f(x)=(x+9)(x^{2}-9)
inverse oflaplace 6/(s^4(s-2)^2)	inverselaplace\:\frac{6}{s^{4}(s-2)^{2}}
integral of ((x+2))/(x(x^2+4))	\int\:\frac{(x+2)}{x(x^{2}+4)}dx
derivative of 2sec^2(5pix-1)	\frac{d}{dx}(2\sec^{2}(5πx-1))
derivative of 5/x+x/5	\frac{d}{dx}(\frac{5}{x}+\frac{x}{5})
(dy)/(dx)=sqrt(16x+y)-16	\frac{dy}{dx}=\sqrt{16x+y}-16
integral of xln(1/x)	\int\:x\ln(\frac{1}{x})dx
slope of (1.1)(2.4)	slope\:(1.1)(2.4)
tangent of 5x-4sqrt(x)	tangent\:5x-4\sqrt{x}
integral of 9tan^2(x)sec(x)	\int\:9\tan^{2}(x)\sec(x)dx
(\partial)/(\partial y)(sqrt(x^2+y^2)-z)	\frac{\partial\:}{\partial\:y}(\sqrt{x^{2}+y^{2}}-z)
integral of (e^{6x})/(e^{6x)+7}	\int\:\frac{e^{6x}}{e^{6x}+7}dx
integral of (2x^2)/(20-5x^3)	\int\:\frac{2x^{2}}{20-5x^{3}}dx
tangent of x+1/x	tangent\:x+\frac{1}{x}
simplify x^2In(x)	simplify\:x^{2}In(x)
sum from n=1 to infinity of (70)/(7^n)	\sum\:_{n=1}^{\infty\:}\frac{70}{7^{n}}
integral from 0 to 3 of 30(25-t^2)	\int\:_{0}^{3}30(25-t^{2})dt
limit as x approaches infinity of \|x+2\|	\lim\:_{x\to\:\infty\:}(\left\|x+2\right\|)
integral from 0 to infinity of 1/(2x+5)	\int\:_{0}^{\infty\:}\frac{1}{2x+5}dx
integral from 0 to 1 of 1/(2t^2-2t+1)	\int\:_{0}^{1}\frac{1}{2t^{2}-2t+1}dt
taylor 1/(1-x^2),0	taylor\:\frac{1}{1-x^{2}},0
derivative of-x/5	\frac{d}{dx}(-\frac{x}{5})
limit as x approaches 2 of 3x^3-5x	\lim\:_{x\to\:2}(3x^{3}-5x)
integral from 100 to 120 of (600)/x	\int\:_{100}^{120}\frac{600}{x}dx
tangent of f(x)=4x^2-x^3,\at x=1	tangent\:f(x)=4x^{2}-x^{3},\at\:x=1
(dy)/(dx)+2y=3	\frac{dy}{dx}+2y=3
limit as x approaches 0 of 1/2 x^2	\lim\:_{x\to\:0}(\frac{1}{2}x^{2})
limit as x approaches 1 of 3x+5	\lim\:_{x\to\:1}(3x+5)
(\partial)/(\partial y)(x/(x^7-y^3))	\frac{\partial\:}{\partial\:y}(\frac{x}{x^{7}-y^{3}})
derivative of (3x^2+1/(x+2))	\frac{d}{dx}(\frac{3x^{2}+1}{x+2})
integral of (x+2)/((3+2x-x^2)^{3/2)}	\int\:\frac{x+2}{(3+2x-x^{2})^{\frac{3}{2}}}dx
derivative of ae^{bx}	\frac{d}{dx}(ae^{bx})
integral of (100)/(7x-16)	\int\:\frac{100}{7x-16}dx
derivative of 4/(x+2sqrt(x))	\frac{d}{dx}(\frac{4}{x+2\sqrt{x}})
f(x)=3x^{2/3}	f(x)=3x^{\frac{2}{3}}
derivative of ({g}(x)/(sqrt(x)))	\frac{d}{dx}(\frac{{g}(x)}{\sqrt{x}})
integral of-4y^2	\int\:-4y^{2}dy
(\partial)/(\partial x)((x+y)^3)	\frac{\partial\:}{\partial\:x}((x+y)^{3})
(\partial)/(\partial x)(x^2yz-xyz^3)	\frac{\partial\:}{\partial\:x}(x^{2}yz-xyz^{3})
area y=7x,y=x^2-8	area\:y=7x,y=x^{2}-8
derivative of f(x)=sqrt(x/(x+9))	derivative\:f(x)=\sqrt{\frac{x}{x+9}}
derivative of (2x+3(2x-3))	\frac{d}{dx}((2x+3)(2x-3))
derivative of-x^2+3x	\frac{d}{dx}(-x^{2}+3x)
limit as x approaches infinity of 1/(x^{4/3)}	\lim\:_{x\to\:\infty\:}(\frac{1}{x^{\frac{4}{3}}})
d/(dy)(x/(y^2+x^2))	\frac{d}{dy}(\frac{x}{y^{2}+x^{2}})
y^{''}-4y^'-5y=0,y(1)=0,y^'(1)=4	y^{\prime\:\prime\:}-4y^{\prime\:}-5y=0,y(1)=0,y^{\prime\:}(1)=4
integral of (2+x)/(4x^2-4x-3)	\int\:\frac{2+x}{4x^{2}-4x-3}dx
derivative of f(x)=ln(x-1)	derivative\:f(x)=\ln(x-1)
integral of (12x^2-8x+2)	\int\:(12x^{2}-8x+2)dx
(dy}{dx}=\frac{(x-1))/y	\frac{dy}{dx}=\frac{(x-1)}{y}
derivative of 7arcsin(x^2)	\frac{d}{dx}(7\arcsin(x^{2}))
integral of (sqrt(2y^2-3))/(y^2)	\int\:\frac{\sqrt{2y^{2}-3}}{y^{2}}dy
derivative of (2x^{4x})	\frac{d}{dx}((2x)^{4x})
integral of (x^2+5)	\int\:(x^{2}+5)dx
integral of (sqrt(x+1))/x	\int\:\frac{\sqrt{x+1}}{x}dx
y^'=4y^2+1	y^{\prime\:}=4y^{2}+1
integral of cos(k)x	\int\:\cos(k)xdx

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