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Popular Calculus Problems

derivative of f(x)= 4/3 x-7	derivative\:f(x)=\frac{4}{3}x-7
(d^3)/(dx^3)(1/(x^2))	\frac{d^{3}}{dx^{3}}(\frac{1}{x^{2}})
(\partial)/(\partial x)((1-x)^2)	\frac{\partial\:}{\partial\:x}((1-x)^{2})
d/(dt)((ce^t)/(1+ce^t))	\frac{d}{dt}(\frac{ce^{t}}{1+ce^{t}})
(dy)/(dt)=((y+1))/((t+1))	\frac{dy}{dt}=\frac{(y+1)}{(t+1)}
integral from 4 to 9 of (x-3)/(sqrt(x))	\int\:_{4}^{9}\frac{x-3}{\sqrt{x}}dx
integral of sec^4(xta)n^2x	\int\:\sec^{4}(xta)n^{2}xdx
integral of x/(sqrt(1+x))	\int\:\frac{x}{\sqrt{1+x}}dx
limit as x approaches 1 of 1/((x-1))	\lim\:_{x\to\:1}(\frac{1}{(x-1)})
integral of 5sin(2t)	\int\:5\sin(2t)dt
derivative of f(3)=-2/((x-2)^2)	derivative\:f(3)=-\frac{2}{(x-2)^{2}}
(d^2)/(dx^2)(5x^2)	\frac{d^{2}}{dx^{2}}(5x^{2})
(\partial)/(\partial z)(sin(y)cos(x))	\frac{\partial\:}{\partial\:z}(\sin(y)\cos(x))
derivative of arctanh(\sqrt[4]{x})	\frac{d}{dx}(\arctanh(\sqrt[4]{x}))
derivative of 2x-17	derivative\:2x-17
integral of sin(t)-cos(t)	\int\:\sin(t)-\cos(t)dt
limit as x approaches 2 of ln(x-2)	\lim\:_{x\to\:2}(\ln(x-2))
limit as x approaches-1 of 30	\lim\:_{x\to\:-1}(30)
(\partial)/(\partial x)(3x^2y^2-3)	\frac{\partial\:}{\partial\:x}(3x^{2}y^{2}-3)
derivative of (2-x-3x^3)(7+x^5)	derivative\:(2-x-3x^{3})(7+x^{5})
derivative of (s^{(-1)/2}+7s)(1-s^{-1})	derivative\:(s^{\frac{-1}{2}}+7s)(1-s^{-1})
derivative of (2-x^3^3)	\frac{d}{dx}((2-x^{3})^{3})
limit as x approaches-3 of sqrt(19+x)	\lim\:_{x\to\:-3}(\sqrt{19+x})
tangent of x^2e^x-2xe^x+2e^x	tangent\:x^{2}e^{x}-2xe^{x}+2e^{x}
derivative of 8x^4	derivative\:8x^{4}
derivative of sin(x-x^2)	\frac{d}{dx}(\sin(x-x^{2}))
integral of 5sin^4(x)cos^2(x)	\int\:5\sin^{4}(x)\cos^{2}(x)dx
integral of 3/(50+2x)	\int\:\frac{3}{50+2x}dx
y^{''}+6y^'+8y=e^{-5x}	y^{\prime\:\prime\:}+6y^{\prime\:}+8y=e^{-5x}
derivative of 6x^{70}	\frac{d}{dx}(6x^{70})
y^{''}-y^'-2y=-2t+10t^2	y^{\prime\:\prime\:}-y^{\prime\:}-2y=-2t+10t^{2}
integral of 1/(5x+16)	\int\:\frac{1}{5x+16}dx
area y=9x^2,y=x^2+7	area\:y=9x^{2},y=x^{2}+7
limit as h approaches 0 of 2xh	\lim\:_{h\to\:0}(2xh)
sum from n=5 to infinity of 1/(n^2)	\sum\:_{n=5}^{\infty\:}\frac{1}{n^{2}}
integral of (1/y sin(x/y)+x)	\int\:(\frac{1}{y}\sin(\frac{x}{y})+x)dx
derivative of arctan(e^x+1)	\frac{d}{dx}(\arctan(e^{x}+1))
integral from-1 to 2 of (x^2-x-2)	\int\:_{-1}^{2}(x^{2}-x-2)dx
limit as x approaches-5 of (x^2)/(5-x)	\lim\:_{x\to\:-5}(\frac{x^{2}}{5-x})
derivative of 9/(x^4)	\frac{d}{dx}(\frac{9}{x^{4}})
area 3x^2,-3x+6,-4,2	area\:3x^{2},-3x+6,-4,2
limit as x approaches 0+of (x+92)/x	\lim\:_{x\to\:0+}(\frac{x+92}{x})
derivative of-a/x	\frac{d}{dx}(-\frac{a}{x})
integral of (e^x)/(sqrt(1+e^x))	\int\:\frac{e^{x}}{\sqrt{1+e^{x}}}dx
integral of x^9sqrt(x^5+3)	\int\:x^{9}\sqrt{x^{5}+3}dx
derivative of ln((5x^2))	\frac{d}{dx}(\ln((5x)^{2}))
y^{''}+7y^'=0	y^{\prime\:\prime\:}+7y^{\prime\:}=0
derivative of cot(3-2x)	\frac{d}{dx}(\cot(3-2x))
(d^2y)/(dt^2)+5(dy)/(dt)+6y=1	\frac{d^{2}y}{dt^{2}}+5\frac{dy}{dt}+6y=1
xy^2y^'=y^3-4x^3,y(1)=4	xy^{2}y^{\prime\:}=y^{3}-4x^{3},y(1)=4
inverse oflaplace ((-1/4))/(1+(1/2)*s)	inverselaplace\:\frac{(-\frac{1}{4})}{1+(\frac{1}{2})\cdot\:s}
derivative of (arctan(x)^2)	\frac{d}{dx}((\arctan(x))^{2})
limit as x approaches 1+of 1/(x+8)	\lim\:_{x\to\:1+}(\frac{1}{x+8})
(\partial)/(\partial x)(-6ysin(3x))	\frac{\partial\:}{\partial\:x}(-6y\sin(3x))
integral of 1/(xsqrt(4x^2+25))	\int\:\frac{1}{x\sqrt{4x^{2}+25}}dx
y=3cos(x)sin(x)	y=3\cos(x)\sin(x)
derivative of 8arcsin(e^{x/2})	derivative\:8\arcsin(e^{\frac{x}{2}})
inverse oflaplace s/(s^2(s^2+1))	inverselaplace\:\frac{s}{s^{2}(s^{2}+1)}
d/(dt)(e^{2t})	\frac{d}{dt}(e^{2t})
maclaurin (1-x)^{-1/2},4	maclaurin\:(1-x)^{-\frac{1}{2}},4
slope of y=x^2-3	slope\:y=x^{2}-3
f(x)=xsin(4/x)	f(x)=x\sin(\frac{4}{x})
derivative of 3x^2-e^{-x}	\frac{d}{dx}(3x^{2}-e^{-x})
area x=y^2,x=y^2+2	area\:x=y^{2},x=y^{2}+2
derivative of arcsin(cos(x^3))	derivative\:\arcsin(\cos(x^{3}))
tangent of f(x)=3x-2sqrt(x),\at x=1	tangent\:f(x)=3x-2\sqrt{x},\at\:x=1
(\partial)/(\partial y)((9y)/(x^5))	\frac{\partial\:}{\partial\:y}(\frac{9y}{x^{5}})
y^{''}+22y=0	y^{\prime\:\prime\:}+22y=0
(\partial)/(\partial y)(x^2+xy+y^2)	\frac{\partial\:}{\partial\:y}(x^{2}+xy+y^{2})
area 10-7x,y=0,x^2-20	area\:10-7x,y=0,x^{2}-20
integral of 2x+3x^{-2}	\int\:2x+3x^{-2}dx
integral of (5sin^3(sqrt(x)))/(sqrt(x))	\int\:\frac{5\sin^{3}(\sqrt{x})}{\sqrt{x}}dx
(dy)/(dt)+2y=3e^t,y(0)=1	\frac{dy}{dt}+2y=3e^{t},y(0)=1
derivative of y=ln(x^4)	derivative\:y=\ln(x^{4})
integral of sqrt(4+5x^2)	\int\:\sqrt{4+5x^{2}}dx
integral of 1/(x*sqrt(x)+x^2)	\int\:\frac{1}{x\cdot\:\sqrt{x}+x^{2}}dx
integral from 0 to e of xln(x)	\int\:_{0}^{e}x\ln(x)dx
y^'=(x-2)(y-2)	y^{\prime\:}=(x-2)(y-2)
tangent of f(x)=-x+5x^{-1/2}-3,(1,1)	tangent\:f(x)=-x+5x^{-\frac{1}{2}}-3,(1,1)
(dy)/(dx)=((x-3))/(y-3)	\frac{dy}{dx}=\frac{(x-3)}{y-3}
integral from 0 to infinity of 1/(1+x)	\int\:_{0}^{\infty\:}\frac{1}{1+x}dx
integral of 2cos^2(θ)	\int\:2\cos^{2}(θ)dθ
derivative of (e^x+e^{-x}/(e^x-e^{-x)})	\frac{d}{dx}(\frac{e^{x}+e^{-x}}{e^{x}-e^{-x}})
(d^3)/(dx^3)(x^2sin(sqrt(x)))	\frac{d^{3}}{dx^{3}}(x^{2}\sin(\sqrt{x}))
derivative of (a-x^2)	\frac{d}{dx}((a-x)^{2})
derivative of (x^5/(a+b)-(x^2)/(a-b))	\frac{d}{dx}(\frac{x^{5}}{a+b}-\frac{x^{2}}{a-b})
derivative of 0.7x^2	\frac{d}{dx}(0.7x^{2})
derivative of 1/(-2x^2)	\frac{d}{dx}(\frac{1}{-2x^{2}})
sum from n=0 to infinity of (2x)^n	\sum\:_{n=0}^{\infty\:}(2x)^{n}
tangent of f(x)=x2^x	tangent\:f(x)=x2^{x}
slope of (-2.3)(2.2)	slope\:(-2.3)(2.2)
limit as x approaches 0-of x*arctan(1/x)	\lim\:_{x\to\:0-}(x\cdot\:\arctan(\frac{1}{x}))
(dy)/(dx)=(2x)/(1+2y),y(2)=0	\frac{dy}{dx}=\frac{2x}{1+2y},y(2)=0
sum from n=1 to infinity}(-1)^{n-1 of (2^n)/(n^4)	\sum\:_{n=1}^{\infty\:}(-1)^{n-1}\frac{2^{n}}{n^{4}}
limit as x approaches 4 of 2^x	\lim\:_{x\to\:4}(2^{x})
integral of (sin(5x))/(16+cos^2(5x))	\int\:\frac{\sin(5x)}{16+\cos^{2}(5x)}dx
(\partial)/(\partial x)(6x+5sqrt(y))	\frac{\partial\:}{\partial\:x}(6x+5\sqrt{y})
integral of (24t+6t^3)/(8t^2+t^4)	\int\:\frac{24t+6t^{3}}{8t^{2}+t^{4}}dt
laplacetransform e^{-2t-3}	laplacetransform\:e^{-2t-3}
derivative of sqrt(x/pi)	\frac{d}{dx}(\sqrt{\frac{x}{π}})

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