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Popular Calculus Problems

derivative of f(x)=-(13)/(x^4)	derivative\:f(x)=-\frac{13}{x^{4}}
integral of ((2x+3))/((x+1)^2)	\int\:\frac{(2x+3)}{(x+1)^{2}}dx
tangent of 110x-16x^2	tangent\:110x-16x^{2}
derivative of 16	\frac{d}{dx}(16)
integral of (7-6x^3+4x^6)/(x^6)	\int\:\frac{7-6x^{3}+4x^{6}}{x^{6}}dx
derivative of arctan(1/(3x))	\frac{d}{dx}(\arctan(\frac{1}{3x}))
d/(d{r)}(({r})/(sqrt({r)^2+5)})	\frac{d}{d{r}}(\frac{{r}}{\sqrt{{r}^{2}+5}})
limit as t approaches 3 of (2t-3)/(t-3)	\lim\:_{t\to\:3}(\frac{2t-3}{t-3})
slope of y=5sec(x)-10cos(x),(pi/3 ,5)	slope\:y=5\sec(x)-10\cos(x),(\frac{π}{3},5)
derivative of y=arcsin(3sqrt(5x))	derivative\:y=\arcsin(3\sqrt{5x})
limit as x approaches 1 of 2sqrt(3x^2+1)	\lim\:_{x\to\:1}(2\sqrt{3x^{2}+1})
(\partial)/(\partial z)(2xyz^{-1})	\frac{\partial\:}{\partial\:z}(2xyz^{-1})
integral of (3x^2)/(sqrt(1-x^3))	\int\:\frac{3x^{2}}{\sqrt{1-x^{3}}}dx
y^2dx+(2xy+1)dy=0,y(9)=90	y^{2}dx+(2xy+1)dy=0,y(9)=90
limit as x approaches 0+of tan^x(2x)	\lim\:_{x\to\:0+}(\tan^{x}(2x))
derivative of-ax-d/(x^2)	\frac{d}{dx}(-ax-\frac{d}{x^{2}})
integral of e^{-x}*ln(x)	\int\:e^{-x}\cdot\:\ln(x)dx
integral of (sec(x))/(sec(x)+tan(x))	\int\:\frac{\sec(x)}{\sec(x)+\tan(x)}dx
derivative of (ln(x))^2	derivative\:(\ln(x))^{2}
integral from 1 to 2 of x*ln(x)	\int\:_{1}^{2}x\cdot\:\ln(x)dx
integral of 1/(4+5x^6)(30x^5)	\int\:\frac{1}{4+5x^{6}}(30x^{5})dx
derivative of x(2x+7)^{1/3}	derivative\:x(2x+7)^{\frac{1}{3}}
t^2y^{''}+6ty^'-6y=0	t^{2}y^{\prime\:\prime\:}+6ty^{\prime\:}-6y=0
(\partial)/(\partial x)((x^3-y^2)^{(-1)})	\frac{\partial\:}{\partial\:x}((x^{3}-y^{2})^{(-1)})
derivative of 4x^2+3x+2	\frac{d}{dx}(4x^{2}+3x+2)
derivative of y=e^e	derivative\:y=e^{e}
integral of x^2(1-x)	\int\:x^{2}(1-x)dx
integral of (sin(x))/(sqrt(x))	\int\:\frac{\sin(x)}{\sqrt{x}}dx
integral from 0 to 1 of 1/((2x-3)^2)	\int\:_{0}^{1}\frac{1}{(2x-3)^{2}}dx
derivative of (192/(x^4))	\frac{d}{dx}(\frac{192}{x^{4}})
derivative of sin^2(cos(4x))	\frac{d}{dx}(\sin^{2}(\cos(4x)))
(dy)/(dx)=sqrt(13x+y)-13	\frac{dy}{dx}=\sqrt{13x+y}-13
integral from 0 to pi of x^2cos(x)	\int\:_{0}^{π}x^{2}\cos(x)dx
integral of (4x^2+13x-9)/(x^3+2x^2-3x)	\int\:\frac{4x^{2}+13x-9}{x^{3}+2x^{2}-3x}dx
(dy)/(dt)+3y=cos(2t),y(0)=-1	\frac{dy}{dt}+3y=\cos(2t),y(0)=-1
integral of (a+bsin^3(t))/(cos^2(t))	\int\:\frac{a+b\sin^{3}(t)}{\cos^{2}(t)}dt
integral of-32x	\int\:-32xdx
integral from 0 to 2 of 1/(x^2-6x+5)	\int\:_{0}^{2}\frac{1}{x^{2}-6x+5}dx
derivative of arctan(x-pi/4)	\frac{d}{dx}(\arctan(x)-\frac{π}{4})
tangent of f(x)=3sin(x)	tangent\:f(x)=3\sin(x)
inverse oflaplace (10)/(2s+1)	inverselaplace\:\frac{10}{2s+1}
integral of ((x+5))/((x^2+16))	\int\:\frac{(x+5)}{(x^{2}+16)}dx
integral of 1/(sqrt(x^3))	\int\:\frac{1}{\sqrt{x^{3}}}dx
x^2y^{''}-3xy^'+3y=0	x^{2}y^{\prime\:\prime\:}-3xy^{\prime\:}+3y=0
slope of x^2-3x-4	slope\:x^{2}-3x-4
derivative of y=7x^3	derivative\:y=7x^{3}
integral of (x^2)/(1-x^6)	\int\:\frac{x^{2}}{1-x^{6}}dx
integral of sqrt(x)cos(sqrt(x))	\int\:\sqrt{x}\cos(\sqrt{x})dx
limit as x approaches-7 of (6x+42)/(x+7)	\lim\:_{x\to\:-7}(\frac{6x+42}{x+7})
tangent of f(x)=3x^3+4x^2,(-1,1)	tangent\:f(x)=3x^{3}+4x^{2},(-1,1)
derivative of 7^{2x}	\frac{d}{dx}(7^{2x})
derivative of y= 1/4 x^2-1/2 ln(x)	derivative\:y=\frac{1}{4}x^{2}-\frac{1}{2}\ln(x)
(\partial)/(\partial y)(2xe^y)	\frac{\partial\:}{\partial\:y}(2xe^{y})
tangent of 15-x^2	tangent\:15-x^{2}
d/(dt)((1-3t^2)/(1-2t))	\frac{d}{dt}(\frac{1-3t^{2}}{1-2t})
derivative of (-pix^2-4x^2+64x/8)	\frac{d}{dx}(\frac{-πx^{2}-4x^{2}+64x}{8})
integral of 4/(x^5)-5x^4	\int\:\frac{4}{x^{5}}-5x^{4}dx
(\partial)/(\partial y)(ln(x^6y))	\frac{\partial\:}{\partial\:y}(\ln(x^{6}y))
sum from n=0 to infinity of (2/3)^n	\sum\:_{n=0}^{\infty\:}(\frac{2}{3})^{n}
derivative of xln^3(x)	\frac{d}{dx}(x\ln^{3}(x))
integral of (11x^3)/(sqrt(9+x^2))	\int\:\frac{11x^{3}}{\sqrt{9+x^{2}}}dx
integral of 1/((x-3)(x-2))	\int\:\frac{1}{(x-3)(x-2)}dx
(\partial)/(\partial x)(sqrt(2x^2-5y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{2x^{2}-5y^{2}})
integral from-2 to 6 of 4x-x^2+12	\int\:_{-2}^{6}4x-x^{2}+12dx
y^{''}+5y^'=e^{-t},y(0)=0,y^'(0)=1	y^{\prime\:\prime\:}+5y^{\prime\:}=e^{-t},y(0)=0,y^{\prime\:}(0)=1
limit as x approaches 4 of f(x)	\lim\:_{x\to\:4}(f(x))
f(x)=-1/x	f(x)=-\frac{1}{x}
integral of 1/(x^2+2x+1)	\int\:\frac{1}{x^{2}+2x+1}dx
integral of (x^4)/(sqrt(x^2-9))	\int\:\frac{x^{4}}{\sqrt{x^{2}-9}}dx
4x^2y^'=y^'+6xe^{-y}	4x^{2}y^{\prime\:}=y^{\prime\:}+6xe^{-y}
derivative of 6xe^x	\frac{d}{dx}(6xe^{x})
tangent of f(x)=x^3-3x^2+2x-2,\at x=0	tangent\:f(x)=x^{3}-3x^{2}+2x-2,\at\:x=0
(\partial)/(\partial y)((3x-4y)/(3x+4y))	\frac{\partial\:}{\partial\:y}(\frac{3x-4y}{3x+4y})
limit as x approaches 9 of cos(1/(x-9))	\lim\:_{x\to\:9}(\cos(\frac{1}{x-9}))
derivative of \sqrt[3]{6x}	derivative\:\sqrt[3]{6x}
integral of 4sin(x/2)+8	\int\:4\sin(\frac{x}{2})+8dx
integral of csc^6(x)	\int\:\csc^{6}(x)dx
taylor ((1-v))/((1+v))	taylor\:\frac{(1-v)}{(1+v)}
derivative of f(x)=(0.001+2)^{0.001}	derivative\:f(x)=(0.001+2)^{0.001}
limit as x approaches infinity of e^{-8x^2}	\lim\:_{x\to\:\infty\:}(e^{-8x^{2}})
integral of ((2x+5))/(sqrt(x^2+5x))	\int\:\frac{(2x+5)}{\sqrt{x^{2}+5x}}dx
derivative of (csc(xtan(x))/(cos(x)))	\frac{d}{dx}(\frac{\csc(x)\tan(x)}{\cos(x)})
limit as x approaches 5 of 5x-4	\lim\:_{x\to\:5}(5x-4)
integral of (x^4+x-9)/(x^2+3)	\int\:\frac{x^{4}+x-9}{x^{2}+3}dx
(\partial)/(\partial x)(x^3+y^3+z^3+6xyz)	\frac{\partial\:}{\partial\:x}(x^{3}+y^{3}+z^{3}+6xyz)
integral of (3-4x^3+6x^6)/(x^6)	\int\:\frac{3-4x^{3}+6x^{6}}{x^{6}}dx
-y^{'''}+2y^{''}+3y^'+3=0	-y^{\prime\:\prime\:\prime\:}+2y^{\prime\:\prime\:}+3y^{\prime\:}+3=0
derivative of ln(x+2y)	\frac{d}{dx}(\ln(x+2y))
derivative of cot(11x)	\frac{d}{dx}(\cot(11x))
integral from 2 to 5 of 4	\int\:_{2}^{5}4dx
derivative of y=(7sqrt(x))/x	derivative\:y=\frac{7\sqrt{x}}{x}
integral from 3 to 5 of 1/((x-4)^2)	\int\:_{3}^{5}\frac{1}{(x-4)^{2}}dx
(\partial)/(\partial x)((x-3y)/(2xy+3))	\frac{\partial\:}{\partial\:x}(\frac{x-3y}{2xy+3})
(\partial)/(\partial x)(3-3x+4y-4x^2y)	\frac{\partial\:}{\partial\:x}(3-3x+4y-4x^{2}y)
derivative of (45/(0.01x^2+1))	\frac{d}{dx}(\frac{45}{0.01x^{2}+1})
integral of 3cos(sqrt(10x))	\int\:3\cos(\sqrt{10x})dx
derivative of log_{5}(x^4sqrt(2x^2+9x))	\frac{d}{dx}(\log_{5}(x^{4}\sqrt{2x^{2}+9x}))
derivative of (2x-1/(3x^2))	\frac{d}{dx}(\frac{2x-1}{3x^{2}})
xy^'=y+xe^{y/x}	xy^{\prime\:}=y+xe^{\frac{y}{x}}
integral from-4 to 2 of-x^2-2x+8	\int\:_{-4}^{2}-x^{2}-2x+8dx

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