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Popular Calculus Problems

derivative of xsin(9/x)	\frac{d}{dx}(x\sin(\frac{9}{x}))
integral of 3sin(t)+2cos(t)+2	\int\:3\sin(t)+2\cos(t)+2dt
area sqrt(x+2), 1/(x+1),[0,2]	area\:\sqrt{x+2},\frac{1}{x+1},[0,2]
integral of cos^7(x)tan^6(x)	\int\:\cos^{7}(x)\tan^{6}(x)dx
integral of (8-4x)e^{2x}	\int\:(8-4x)e^{2x}dx
(dy)/(dx)-4tan(2x)y=sin(2x)	\frac{dy}{dx}-4\tan(2x)y=\sin(2x)
derivative of px+b	\frac{d}{dx}(px+b)
limit as x approaches 1+of 4/(1-x)	\lim\:_{x\to\:1+}(\frac{4}{1-x})
integral of x^2*\sqrt[3]{1-x}	\int\:x^{2}\cdot\:\sqrt[3]{1-x}dx
integral of sqrt(3)	\int\:\sqrt{3}dx
tangent of y=arctan(-x),\at x=4	tangent\:y=\arctan(-x),\at\:x=4
derivative of y=x^4e^{2x}	derivative\:y=x^{4}e^{2x}
limit as x approaches 0+of 4/x-4/(\|x\|)	\lim\:_{x\to\:0+}(\frac{4}{x}-\frac{4}{\left\|x\right\|})
slope of (790,77880),(970,94440)	slope\:(790,77880),(970,94440)
integral of 3/37 x^2	\int\:\frac{3}{37}x^{2}dx
derivative of 9/(4\sqrt[4]{x^3})	\frac{d}{dx}(\frac{9}{4\sqrt[4]{x^{3}}})
integral of (2x^2-x)/(x^2-x+2)	\int\:\frac{2x^{2}-x}{x^{2}-x+2}dx
integral of 2xe^x	\int\:2xe^{x}dx
integral of (2x-1)y^2sin(4xy)	\int\:(2x-1)y^{2}\sin(4xy)dx
derivative of f(x)=8x-3	derivative\:f(x)=8x-3
tangent of f(x)=2e^xcos(x),\at x=0	tangent\:f(x)=2e^{x}\cos(x),\at\:x=0
integral of ((1+1/x)^3(1/(x^2)))	\int\:((1+\frac{1}{x})^{3}(\frac{1}{x^{2}}))dx
taylor sqrt(8+x^2)	taylor\:\sqrt{8+x^{2}}
f(t)=-cos(t)	f(t)=-\cos(t)
derivative of ln(5-x)	derivative\:\ln(5-x)
derivative of f(x)= 2/(3+x)	derivative\:f(x)=\frac{2}{3+x}
derivative of 1/(x^2-25)	\frac{d}{dx}(\frac{1}{x^{2}-25})
y^{''}+25y=sin(5x)	y^{\prime\:\prime\:}+25y=\sin(5x)
integral of sec^2(x)+9	\int\:\sec^{2}(x)+9dx
integral of-(5^{-x})/(ln(5))	\int\:-\frac{5^{-x}}{\ln(5)}dx
integral of-36x^2-18x-4	\int\:-36x^{2}-18x-4dx
y^{''}+2y^'-8y=2e^{-3x}-e^{-x}	y^{\prime\:\prime\:}+2y^{\prime\:}-8y=2e^{-3x}-e^{-x}
sum from n=0 to infinity of (x-2)^n	\sum\:_{n=0}^{\infty\:}(x-2)^{n}
(\partial)/(\partial y)(e^{-x}sin(y)z)	\frac{\partial\:}{\partial\:y}(e^{-x}\sin(y)z)
d/(da)(4sin(3a)cos(3a))	\frac{d}{da}(4\sin(3a)\cos(3a))
limit as x approaches 0+of 8/(x^2-x)	\lim\:_{x\to\:0+}(\frac{8}{x^{2}-x})
slope ofintercept (8.4)(4.1)	slopeintercept\:(8.4)(4.1)
limit as x approaches-1-of f(x)	\lim\:_{x\to\:-1-}(f(x))
derivative of (sqrt(a^2+x^2)/x)	\frac{d}{dx}(\frac{\sqrt{a^{2}+x^{2}}}{x})
(\partial)/(\partial x)(x^2y-xy^3)	\frac{\partial\:}{\partial\:x}(x^{2}y-xy^{3})
derivative of e^{3x}+1	\frac{d}{dx}(e^{3x}+1)
integral of 100q^{-0.5}	\int\:100q^{-0.5}dq
derivative of sqrt(24x)	derivative\:\sqrt{24x}
tangent of f(x)=(x-1)/(x+1)	tangent\:f(x)=\frac{x-1}{x+1}
derivative of sqrt(7-5x)	\frac{d}{dx}(\sqrt{7-5x})
limit as x approaches 0 of sqrt(x^2+2)	\lim\:_{x\to\:0}(\sqrt{x^{2}+2})
integral of (10)/(e^{x/4)}	\int\:\frac{10}{e^{\frac{x}{4}}}dx
integral of (sin(2x+y)-sin(x+y))	\int\:(\sin(2x+y)-\sin(x+y))dx
integral of (2y(x-1))/(y^2+1)	\int\:\frac{2y(x-1)}{y^{2}+1}dy
area 20x-50,y=0,2x^2	area\:20x-50,y=0,2x^{2}
integral of (4-r^2)r	\int\:(4-r^{2})rdr
derivative of f(x)=9sqrt(x)	derivative\:f(x)=9\sqrt{x}
limit as n approaches infinity of n^n	\lim\:_{n\to\:\infty\:}(n^{n})
derivative of 8x+2	\frac{d}{dx}(8x+2)
integral of 2^{2x}	\int\:2^{2x}dx
derivative of-(24/(x^4))	\frac{d}{dx}(-\frac{24}{x^{4}})
area y=x(x^2-10x+30),y=x^2	area\:y=x(x^{2}-10x+30),y=x^{2}
integral of xe^{-125x}	\int\:xe^{-125x}dx
area x^2+x+23,2x^2+3	area\:x^{2}+x+23,2x^{2}+3
sum from n=5 to infinity of 1/(27^n)	\sum\:_{n=5}^{\infty\:}\frac{1}{27^{n}}
limit as x approaches 0 of sin(sin(x))	\lim\:_{x\to\:0}(\sin(\sin(x)))
integral of (sin(x))/(sqrt(1+cos^2(x)))	\int\:\frac{\sin(x)}{\sqrt{1+\cos^{2}(x)}}dx
integral from 7 to 9 of (x^2+2x-3)	\int\:_{7}^{9}(x^{2}+2x-3)dx
y^{''}+6y^'+9y=32e^t,y(0)=1,y^'(0)=7	y^{\prime\:\prime\:}+6y^{\prime\:}+9y=32e^{t},y(0)=1,y^{\prime\:}(0)=7
derivative of (x^2+1^x)	\frac{d}{dx}((x^{2}+1)^{x})
f(x)=ln(1+e^x)	f(x)=\ln(1+e^{x})
area \|x\|,x^2-6	area\:\left\|x\right\|,x^{2}-6
y^'+2y=t,y(0)=1	y^{\prime\:}+2y=t,y(0)=1
(dy}{dx}-2y=\frac{2y)/x	\frac{dy}{dx}-2y=\frac{2y}{x}
integral of arccot(10y)	\int\:\arccot(10y)dy
derivative of ((x-5(x^2+5x+25))/(x^3))	\frac{d}{dx}(\frac{(x-5)(x^{2}+5x+25)}{x^{3}})
derivative of 4x^2+4x	\frac{d}{dx}(4x^{2}+4x)
integral of (x+2)/(2x+1)	\int\:\frac{x+2}{2x+1}dx
derivative of ((x-5)/(x+5))^4	derivative\:(\frac{x-5}{x+5})^{4}
10y^{''}+1000y=50cos(8t)	10y^{\prime\:\prime\:}+1000y=50\cos(8t)
derivative of e^{-x}(1-x)	\frac{d}{dx}(e^{-x}(1-x))
derivative of 3pir^2	derivative\:3πr^{2}
derivative of x^2e^{-0.04x}	\frac{d}{dx}(x^{2}e^{-0.04x})
(\partial)/(\partial y)(xe^{-2x})	\frac{\partial\:}{\partial\:y}(xe^{-2x})
(\partial)/(\partial x)(xy^2z)	\frac{\partial\:}{\partial\:x}(xy^{2}z)
integral of (3-x)^3	\int\:(3-x)^{3}dx
normal of y=x^4+8e^x,(0,8)	normal\:y=x^{4}+8e^{x},(0,8)
integral of cos(2x+3)	\int\:\cos(2x+3)dx
derivative of 4-x^3	\frac{d}{dx}(4-x^{3})
(dy)/(dt)= t/(t^2y+y),y(0)=7	\frac{dy}{dt}=\frac{t}{t^{2}y+y},y(0)=7
limit as x approaches 7-of \|x-7\|	\lim\:_{x\to\:7-}(\left\|x-7\right\|)
sum from n=1 to infinity of 7/(n8^n)	\sum\:_{n=1}^{\infty\:}\frac{7}{n8^{n}}
integral from-infinity to-1 of 3/(x^2)	\int\:_{-\infty\:}^{-1}\frac{3}{x^{2}}dx
(dy)/(dx)+y/(x(x-1))=(x-1)	\frac{dy}{dx}+\frac{y}{x(x-1)}=(x-1)
(\partial)/(\partial x)(e^{x^2}+2xy)	\frac{\partial\:}{\partial\:x}(e^{x^{2}}+2xy)
integral of x^{1/2}ln(x)	\int\:x^{\frac{1}{2}}\ln(x)dx
derivative of a+bx^2	\frac{d}{dx}(a+bx^{2})
limit as x approaches-2 of g(x)	\lim\:_{x\to\:-2}(g(x))
area y=e^{-0.6x},y=1.4x+1,x=0,x=5	area\:y=e^{-0.6x},y=1.4x+1,x=0,x=5
derivative of in(x-1)	\frac{d}{dx}(in(x-1))
y^{''}-y=e^{-x}	y^{\prime\:\prime\:}-y=e^{-x}
simplify (3x^2)^{2x}(x^2+2x)^2	simplify\:(3x^{2})^{2x}(x^{2}+2x)^{2}
(\partial)/(\partial x)(((3x-y))/(3x+y))	\frac{\partial\:}{\partial\:x}(\frac{(3x-y)}{3x+y})
integral from 0 to (3pi)/2 of cos^3(5x)	\int\:_{0}^{\frac{3π}{2}}\cos^{3}(5x)dx
integral from 0 to 3 of sqrt(x^2+9)	\int\:_{0}^{3}\sqrt{x^{2}+9}dx

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