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Popular Calculus Problems

taylor 4ln(7+2x^2)	taylor\:4\ln(7+2x^{2})
f(x)= 1/(x^6)	f(x)=\frac{1}{x^{6}}
derivative of sec(x)-6cos(x)	derivative\:\sec(x)-6\cos(x)
(\partial)/(\partial y)(x^y-xy)	\frac{\partial\:}{\partial\:y}(x^{y}-xy)
(dy)/(dx)=2xe^y	\frac{dy}{dx}=2xe^{y}
derivative of (3x^{3x})	\frac{d}{dx}((3x)^{3x})
integral of 1/(a+bx)	\int\:\frac{1}{a+bx}dx
derivative of-4cot(2xcsc(2x))	\frac{d}{dx}(-4\cot(2x)\csc(2x))
y^{''}+2y^'+5y=4sin(2t)	y^{\prime\:\prime\:}+2y^{\prime\:}+5y=4\sin(2t)
derivative of 1/3 cos((6pix-1/2))	\frac{d}{dx}(\frac{1}{3}\cos(\frac{6πx-1}{2}))
integral of x^7sin(x^8)	\int\:x^{7}\sin(x^{8})dx
derivative of e^{x^2}+1	\frac{d}{dx}(e^{x^{2}}+1)
tangent of y=2x^2	tangent\:y=2x^{2}
integral from 0 to y+z of 1/((x+y+z)^3)	\int\:_{0}^{y+z}\frac{1}{(x+y+z)^{3}}dx
derivative of e^x(x-1)	derivative\:e^{x}(x-1)
y^'+sin(t)y=sin(t),y(0)=6	y^{\prime\:}+\sin(t)y=\sin(t),y(0)=6
(\partial)/(\partial x)((x^2-2x)cos(y))	\frac{\partial\:}{\partial\:x}((x^{2}-2x)\cos(y))
derivative of (e^{3x}(cos(2x)))	\frac{d}{dx}((e^{3x})(\cos(2x)))
16y''+8y'+y=0	16y\prime\:\prime\:+8y\prime\:+y=0
limit as x approaches 0 of (tan(4x)cos(6x)-tan(4x))/(24x^3)	\lim\:_{x\to\:0}(\frac{\tan(4x)\cos(6x)-\tan(4x)}{24x^{3}})
limit as x approaches+1 of (x-1)/(x^6-1)	\lim\:_{x\to\:+1}(\frac{x-1}{x^{6}-1})
limit as x approaches 0 of (3x)/(sin(10x))	\lim\:_{x\to\:0}(\frac{3x}{\sin(10x)})
(\partial)/(\partial x)(3(y-1)^3(x-6))	\frac{\partial\:}{\partial\:x}(3(y-1)^{3}(x-6))
integral of (x^3)/(x^2+4x+4)	\int\:\frac{x^{3}}{x^{2}+4x+4}dx
integral of (x-1)^2-4	\int\:(x-1)^{2}-4dx
integral of (x+1)(x+2)	\int\:(x+1)(x+2)dx
limit as x approaches 1 of 1/(x+1)	\lim\:_{x\to\:1}(\frac{1}{x+1})
area f(x)=x^2,x=0,x=2	area\:f(x)=x^{2},x=0,x=2
derivative of (6e^ss-5e^s)/((6s+1)^2)	derivative\:\frac{6e^{s}s-5e^{s}}{(6s+1)^{2}}
integral of (x^3+22)/(x^2+7x+12)	\int\:\frac{x^{3}+22}{x^{2}+7x+12}dx
tangent of y=3e^x+x,(0,3)	tangent\:y=3e^{x}+x,(0,3)
derivative of 2x^2-8	\frac{d}{dx}(2x^{2}-8)
derivative of 7/((7-x^8)^{3/2)}	derivative\:\frac{7}{(7-x^{8})^{\frac{3}{2}}}
derivative of (sin^2(x)+1)^5	derivative\:(\sin^{2}(x)+1)^{5}
derivative of 2t-sin(2t)	derivative\:2t-\sin(2t)
integral of cos^3(x)	\int\:\cos^{3}(x)dx
integral of (x^3+3x)e^{-6x}	\int\:(x^{3}+3x)e^{-6x}dx
(\partial)/(\partial y)(xe^{x^2-y^2})	\frac{\partial\:}{\partial\:y}(xe^{x^{2}-y^{2}})
integral of (4x+3)^9	\int\:(4x+3)^{9}dx
derivative of y=1n(1n(x^3))	derivative\:y=1n(1n(x^{3}))
integral of 7sin^4(x)	\int\:7\sin^{4}(x)dx
derivative of ln(xcos(t))	\frac{d}{dx}(\ln(x)\cos(t))
derivative of cot(e^{2x})	\frac{d}{dx}(\cot(e^{2x}))
y^{''}-6y^'=0	y^{\prime\:\prime\:}-6y^{\prime\:}=0
limit as x approaches 2 of 3x^3-7x^2+3	\lim\:_{x\to\:2}(3x^{3}-7x^{2}+3)
-9x^2y+(dy)/(dx)=-2x^2	-9x^{2}y+\frac{dy}{dx}=-2x^{2}
tangent of ((2x+1))/(x-4)	tangent\:\frac{(2x+1)}{x-4}
derivative of cos^3(1-5x^2)	\frac{d}{dx}(\cos^{3}(1-5x^{2}))
derivative of y=arcsin(5x)	derivative\:y=\arcsin(5x)
derivative of (6x)/(1-cot(x))	derivative\:\frac{6x}{1-\cot(x)}
integral of ((x+1)^3)/((x)^{10)}	\int\:\frac{(x+1)^{3}}{(x)^{10}}dx
derivative of x/(99)	derivative\:\frac{x}{99}
d/(dX)(7.1X+20.3)	\frac{d}{dX}(7.1X+20.3)
derivative of (3x^2-3x+1x^3)	\frac{d}{dx}((3x^{2}-3x+1)x^{3})
integral from 0 to 3 of (3-x)sqrt(x)	\int\:_{0}^{3}(3-x)\sqrt{x}dx
d/(d{y)}({x}(y){z}(y))	\frac{d}{d{y}}({x}(y){z}(y))
taylor xe^{x^2},0	taylor\:xe^{x^{2}},0
integral of (21)/(4+25r^2)	\int\:\frac{21}{4+25r^{2}}dr
derivative of (-1)/((x-1)^2)	derivative\:\frac{-1}{(x-1)^{2}}
derivative of (x^4-2/(x^2-2))	\frac{d}{dx}(\frac{x^{4}-2}{x^{2}-2})
(\partial)/(\partial x)(6x^2y+6xy^3)	\frac{\partial\:}{\partial\:x}(6x^{2}y+6xy^{3})
limit as x approaches-5 of g(x)	\lim\:_{x\to\:-5}(g(x))
d/(d{x)}(({x})/(sqrt({x)^2+{y)^2+{z}^2}})	\frac{d}{d{x}}(\frac{{x}}{\sqrt{{x}^{2}+{y}^{2}+{z}^{2}}})
inverse oflaplace (s+1)/((s^2-2s+5))	inverselaplace\:\frac{s+1}{(s^{2}-2s+5)}
(\partial)/(\partial x)(xyz+xy^5+yz^5+zx^5)	\frac{\partial\:}{\partial\:x}(xyz+xy^{5}+yz^{5}+zx^{5})
area y=x^2-3,y=1	area\:y=x^{2}-3,y=1
integral of \sqrt[3]{e^{4x}+2e^{4x}}	\int\:\sqrt[3]{e^{4x}+2e^{4x}}dx
derivative of x^3-12xy+8y^3	\frac{d}{dx}(x^{3}-12xy+8y^{3})
integral of (x-1)(x+2)	\int\:(x-1)(x+2)dx
derivative of f(x)=5x^{4/5}-2x^{2/7}	derivative\:f(x)=5x^{\frac{4}{5}}-2x^{\frac{2}{7}}
derivative of 1/(x+5)	derivative\:\frac{1}{x+5}
integral of t(2t-3sqrt(t))	\int\:t(2t-3\sqrt{t})dt
(\partial)/(\partial z)(-xyz^2)	\frac{\partial\:}{\partial\:z}(-xyz^{2})
integral of x*\sqrt[4]{x^{11}}	\int\:x\cdot\:\sqrt[4]{x^{11}}dx
integral of 7sec^3(3x)	\int\:7\sec^{3}(3x)dx
integral of (8/3+4u^2)	\int\:(\frac{8}{3}+4u^{2})du
integral of 1/2 \sqrt[3]{x}	\int\:\frac{1}{2}\sqrt[3]{x}dx
(d^2)/(dx^2)(sqrt(1+x))	\frac{d^{2}}{dx^{2}}(\sqrt{1+x})
(\partial)/(\partial y)(cos(8x)sin(2y))	\frac{\partial\:}{\partial\:y}(\cos(8x)\sin(2y))
taylor x^4-3x^2+1	taylor\:x^{4}-3x^{2}+1
sum from n=0 to infinity of 1/(n^3+1)	\sum\:_{n=0}^{\infty\:}\frac{1}{n^{3}+1}
derivative of 7x^{1/5}(x^3-2)	derivative\:7x^{\frac{1}{5}}(x^{3}-2)
derivative of y^2(8-x)	\frac{d}{dx}(y^{2}(8-x))
x^2y^'=4x^2y^3-2xy	x^{2}y^{\prime\:}=4x^{2}y^{3}-2xy
sum from n=1 to infinity of ((3^n))/(n!)	\sum\:_{n=1}^{\infty\:}\frac{(3^{n})}{n!}
laplacetransform cos(4t)cos(6t)	laplacetransform\:\cos(4t)\cos(6t)
integral of 5sin^3(x)cos(x)	\int\:5\sin^{3}(x)\cos(x)dx
derivative of (3-x(2x^2-x))	\frac{d}{dx}((3-x)(2x^{2}-x))
derivative of e^tcos(t)-e^tsin(t)	derivative\:e^{t}\cos(t)-e^{t}\sin(t)
integral of (1-x)/(x^2+1)	\int\:\frac{1-x}{x^{2}+1}dx
(\partial)/(\partial x)(ln(x+sqrt(y)))	\frac{\partial\:}{\partial\:x}(\ln(x+\sqrt{y}))
y^'=e^{(y-x)}	y^{\prime\:}=e^{(y-x)}
((q^4)/4+(2q^3)/3-(11q^2)/2+12q)^'	(\frac{q^{4}}{4}+\frac{2q^{3}}{3}-\frac{11q^{2}}{2}+12q)^{\prime\:}
4(1+x^2)(dy)/(dx)=2xy(y^4-1)	4(1+x^{2})\frac{dy}{dx}=2xy(y^{4}-1)
derivative of f(x)= 3/4 x	derivative\:f(x)=\frac{3}{4}x
derivative of f(x)=(arctan(8x))^2	derivative\:f(x)=(\arctan(8x))^{2}
e^{5y}y^'=x^3	e^{5y}y^{\prime\:}=x^{3}
integral of (5x+1)^{19}	\int\:(5x+1)^{19}dx
limit as x approaches 2+of x/(2-x)	\lim\:_{x\to\:2+}(\frac{x}{2-x})
tangent of y=e^{4x}	tangent\:y=e^{4x}

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