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Popular Calculus Problems

(\partial)/(\partial x)(e^xydy)	\frac{\partial\:}{\partial\:x}(e^{x}\cdot\:y\cdot\:dy)
derivative of e^{-bx}	\frac{d}{dx}(e^{-bx})
integral of 64e^{4x}sin(4x)	\int\:64e^{4x}\sin(4x)dx
integral of (e^y)^2	\int\:(e^{y})^{2}dy
limit as x approaches 0+of 1/(xln(x))	\lim\:_{x\to\:0+}(\frac{1}{x\ln(x)})
integral of 1/(x^6)+3/(x^2)	\int\:\frac{1}{x^{6}}+\frac{3}{x^{2}}dx
derivative of 2xe^x+e^xx^2	derivative\:2xe^{x}+e^{x}x^{2}
derivative of y=e^{-7x^2}	derivative\:y=e^{-7x^{2}}
derivative of 10^{sqrt(x)}	derivative\:10^{\sqrt{x}}
integral from 0 to pi of e^{-st}sin(t)	\int\:_{0}^{π}e^{-st}\sin(t)dt
derivative of (cos(x)/(2+sin(x)))	\frac{d}{dx}(\frac{\cos(x)}{2+\sin(x)})
(dy)/(dx)=e^{4x+2y}	\frac{dy}{dx}=e^{4x+2y}
integral of ((x^2+7)^{2021})x	\int\:((x^{2}+7)^{2021})xdx
integral from 1 to 2 of (x^2+1)/(3x-x^2)	\int\:_{1}^{2}\frac{x^{2}+1}{3x-x^{2}}dx
derivative of (x+(x+sin^2(x)^3)^4)	\frac{d}{dx}((x+(x+\sin^{2}(x))^{3})^{4})
limit as x approaches-4 of (x^2)/(4x+16)	\lim\:_{x\to\:-4}(\frac{x^{2}}{4x+16})
integral from-1/3 to 1/3 of 1/(1-x^2)	\int\:_{-\frac{1}{3}}^{\frac{1}{3}}\frac{1}{1-x^{2}}dx
integral of x/(\sqrt[4]{x)}	\int\:\frac{x}{\sqrt[4]{x}}dx
integral of sin(x^{1/2})	\int\:\sin(x^{\frac{1}{2}})dx
(\partial)/(\partial y)(xln(y))	\frac{\partial\:}{\partial\:y}(x\ln(y))
derivative of e^{-x+1}-x*e^{-x+1}	derivative\:e^{-x+1}-x\cdot\:e^{-x+1}
integral of 14sin^3(x)cos^2(x)	\int\:14\sin^{3}(x)\cos^{2}(x)dx
integral of (5sqrt(x))/(x^3+1)	\int\:\frac{5\sqrt{x}}{x^{3}+1}dx
y^'+2ty^2=0,y(1)= 1/5	y^{\prime\:}+2ty^{2}=0,y(1)=\frac{1}{5}
limit as x approaches 0+of 1/(2x)	\lim\:_{x\to\:0+}(\frac{1}{2x})
integral of (cos(4x))	\int\:(\cos(4x))dx
derivative of (x^3+x^2+x+5ln(5x^2-7))	\frac{d}{dx}((x^{3}+x^{2}+x+5)\ln(5x^{2}-7))
derivative of 8x^{-2}	\frac{d}{dx}(8x^{-2})
integral of (x^5-4x^3)/(sqrt(x))	\int\:\frac{x^{5}-4x^{3}}{\sqrt{x}}dx
inverse oflaplace ((s+5))/((s+3)(s+7))	inverselaplace\:\frac{(s+5)}{(s+3)(s+7)}
derivative of f(x)=2x-(16)/(sqrt(x))	derivative\:f(x)=2x-\frac{16}{\sqrt{x}}
derivative of 6cos(x)+3sin^2(x)	derivative\:6\cos(x)+3\sin^{2}(x)
derivative of 1/(sqrt(2\sqrt{x)})	\frac{d}{dx}(\frac{1}{\sqrt{2}\sqrt{x}})
derivative of 2x+sqrt(x)	\frac{d}{dx}(2x+\sqrt{x})
(dy)/(dt)+e^ty=9e^t	\frac{dy}{dt}+e^{t}y=9e^{t}
(dy)/(dx)=6y^2x	\frac{dy}{dx}=6y^{2}x
normal of y=x^2-5x+3,(2,-3)	normal\:y=x^{2}-5x+3,(2,-3)
sum from n=5 to infinity of 3(0.9)^{n+1}	\sum\:_{n=5}^{\infty\:}3(0.9)^{n+1}
limit as x approaches 0 of x-ln(x)	\lim\:_{x\to\:0}(x-\ln(x))
y^'+y^5x+9y=0	y^{\prime\:}+y^{5}x+9y=0
limit as x approaches-pi/2 of tan(x)	\lim\:_{x\to\:-\frac{π}{2}}(\tan(x))
derivative of sqrt(x)+\sqrt[5]{x}	derivative\:\sqrt{x}+\sqrt[5]{x}
integral of 1/(2e^{2x)}	\int\:\frac{1}{2e^{2x}}dx
integral from 0 to 1 of pi(x-x^3)^2	\int\:_{0}^{1}π(x-x^{3})^{2}dx
tangent of 2x^3-6x^2-18-3	tangent\:2x^{3}-6x^{2}-18-3
area y=-2x^2+6,y=-2	area\:y=-2x^{2}+6,y=-2
integral of 1/(sin^2(x)\sqrt[4]{cot(x))}	\int\:\frac{1}{\sin^{2}(x)\sqrt[4]{\cot(x)}}dx
integral of sqrt(1+x^2)*x^5	\int\:\sqrt{1+x^{2}}\cdot\:x^{5}dx
tangent of y=-x^3+2x^2-4,\at x=-1	tangent\:y=-x^{3}+2x^{2}-4,\at\:x=-1
derivative of-sec^2(x)	derivative\:-\sec^{2}(x)
d/(dn)(e^{nipi})	\frac{d}{dn}(e^{niπ})
y^{''}+y^'+y=0	y^{\prime\:\prime\:}+y^{\prime\:}+y=0
integral of (y^5+5y)	\int\:(y^{5}+5y)dy
y^{''}+y=0,y(pi/3)=16,y^'(pi/3)=-32	y^{\prime\:\prime\:}+y=0,y(\frac{π}{3})=16,y^{\prime\:}(\frac{π}{3})=-32
(\partial)/(\partial y)(7e^{x^2ln(y)})	\frac{\partial\:}{\partial\:y}(7e^{x^{2}\ln(y)})
derivative of 5Y^{5/8}X^{3/8}	derivative\:5Y^{\frac{5}{8}}X^{\frac{3}{8}}
integral of 1/(3x+12)	\int\:\frac{1}{3x+12}dx
(\partial)/(\partial y)(e^{x+y+4})	\frac{\partial\:}{\partial\:y}(e^{x+y+4})
(dy)/(dx)=3y+1	\frac{dy}{dx}=3y+1
derivative of 2+cos(2x)	\frac{d}{dx}(2+\cos(2x))
taylor xsin(x)	taylor\:x\sin(x)
tangent of y=(1+4x)^{3/2}	tangent\:y=(1+4x)^{\frac{3}{2}}
integral of (5sqrt(x+25))/x	\int\:\frac{5\sqrt{x+25}}{x}dx
laplacetransform 3e^t(32t^2+2t+15)	laplacetransform\:3e^{t}(32t^{2}+2t+15)
integral of 3/(e^q+2)	\int\:\frac{3}{e^{q}+2}dq
integral of e^{R/L t}	\int\:e^{\frac{R}{L}t}dt
derivative of f(x)=4x-3x+7	derivative\:f(x)=4x-3x+7
integral of 1/(x^2+2x+101)	\int\:\frac{1}{x^{2}+2x+101}dx
integral of 2/(sqrt(2-x^2))	\int\:\frac{2}{\sqrt{2-x^{2}}}dx
derivative of ln(\sqrt[4]{x})	derivative\:\ln(\sqrt[4]{x})
(\partial)/(\partial x)({f}(x,y))	\frac{\partial\:}{\partial\:x}({f}(x,y))
derivative of (3x/2)	\frac{d}{dx}(\frac{3x}{2})
tangent of sqrt(x-2)	tangent\:\sqrt{x-2}
y^{''}-12y^'+54y=0	y^{\prime\:\prime\:}-12y^{\prime\:}+54y=0
sum from n=2 to infinity of 1/(n^2)	\sum\:_{n=2}^{\infty\:}\frac{1}{n^{2}}
derivative of y=x^{-4}	derivative\:y=x^{-4}
integral of x^3-5x	\int\:x^{3}-5xdx
simplify x/(sqrt(x^2+4))	simplify\:\frac{x}{\sqrt{x^{2}+4}}
(\partial)/(\partial x)(3e^{x-y})	\frac{\partial\:}{\partial\:x}(3e^{x-y})
integral from 6 to 8 of (52)/((x-6)^3)	\int\:_{6}^{8}\frac{52}{(x-6)^{3}}dx
integral of (18x)/(sqrt(1-9x^2))	\int\:\frac{18x}{\sqrt{1-9x^{2}}}dx
integral of (-1)^nx^n	\int\:(-1)^{n}x^{n}dx
integral of y^3(2y^2-3)	\int\:y^{3}(2y^{2}-3)dy
(\partial)/(\partial x)(2y+ye^x)	\frac{\partial\:}{\partial\:x}(2y+ye^{x})
(dx)/(dt)=-3x	\frac{dx}{dt}=-3x
limit as h approaches 0 of (e^{2h}-1)/h	\lim\:_{h\to\:0}(\frac{e^{2h}-1}{h})
tangent of f(x)=2xsqrt(5-2x),\at x=-1	tangent\:f(x)=2x\sqrt{5-2x},\at\:x=-1
integral of r	\int\:rdr
y^'=1+y^2	y^{\prime\:}=1+y^{2}
derivative of f(x)=3x^2-x+3	derivative\:f(x)=3x^{2}-x+3
derivative of (x-17/(sqrt(x)-\sqrt{17)})	\frac{d}{dx}(\frac{x-17}{\sqrt{x}-\sqrt{17}})
integral of sqrt(4-x^2)(16-4x^2)	\int\:\sqrt{4-x^{2}}(16-4x^{2})dx
integral of cos(xz)	\int\:\cos(xz)dx
(dy)/(dx)=0.0012y(2300-y)	\frac{dy}{dx}=0.0012y(2300-y)
integral of (x-5)^2	\int\:(x-5)^{2}dx
derivative of (3x/(2x+1))	\frac{d}{dx}(\frac{3x}{2x+1})
integral of (6x+5)/(6x^2)	\int\:\frac{6x+5}{6x^{2}}dx
sum from n=1 to infinity of-1/n	\sum\:_{n=1}^{\infty\:}-\frac{1}{n}
derivative of x*ln^2(x)	\frac{d}{dx}(x\cdot\:\ln^{2}(x))
integral of 4cos(x)+9sin(x)	\int\:4\cos(x)+9\sin(x)dx

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