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Popular Calculus Problems

(\partial)/(\partial y)(2x^3y+cos(x^2))	\frac{\partial\:}{\partial\:y}(2x^{3}y+\cos(x^{2}))
derivative of Ce^{3x}	\frac{d}{dx}(Ce^{3x})
f(x)=xe^{x^2}	f(x)=xe^{x^{2}}
derivative of 5sin(9x)	\frac{d}{dx}(5\sin(9x))
integral from b to 1 of 6ln(x)	\int\:_{b}^{1}6\ln(x)dx
derivative of sin(2x+cos^2(x))	\frac{d}{dx}(\sin(2x)+\cos^{2}(x))
derivative of 4ln(5x)	\frac{d}{dx}(4\ln(5x))
derivative of (x-4e^{3x})	\frac{d}{dx}((x-4)e^{3x})
limit as x approaches 0 of coth(x)	\lim\:_{x\to\:0}(\coth(x))
derivative of 3x^2+4	derivative\:3x^{2}+4
derivative of 1/(1-x)	derivative\:\frac{1}{1-x}
derivative of (2x^3/(sqrt(x^2-3)))	\frac{d}{dx}(\frac{2x^{3}}{\sqrt{x^{2}-3}})
limit as x approaches 0 of (cot(2x))/(csc(x))	\lim\:_{x\to\:0}(\frac{\cot(2x)}{\csc(x)})
limit as x approaches 0 of ((6^x-8^x))/x	\lim\:_{x\to\:0}(\frac{(6^{x}-8^{x})}{x})
integral of cos(t)+sin(t)	\int\:\cos(t)+\sin(t)dt
sum from n=1 to infinity of 1/(ln(3n))	\sum\:_{n=1}^{\infty\:}\frac{1}{\ln(3n)}
tangent of y= 3/x ,(4, 3/4)	tangent\:y=\frac{3}{x},(4,\frac{3}{4})
derivative of y=96x^2+72x+12	derivative\:y=96x^{2}+72x+12
(\partial)/(\partial y)(e^ysin(xy))	\frac{\partial\:}{\partial\:y}(e^{y}\sin(xy))
integral of (9x)/((2-x^2)^3)	\int\:\frac{9x}{(2-x^{2})^{3}}dx
area y=3x,y=3,x=0	area\:y=3x,y=3,x=0
derivative of arccsc(e^x)	\frac{d}{dx}(\arccsc(e^{x}))
area 7cos(8x),7-7cos(8x),[0, pi/8 ]	area\:7\cos(8x),7-7\cos(8x),[0,\frac{π}{8}]
taylor φ^5cos(φ^2)	taylor\:φ^{5}\cos(φ^{2})
derivative of (2(x+8(x-6))/(x^2-7^2))	\frac{d}{dx}(\frac{2(x+8)(x-6)}{x^{2}-7^{2}})
integral of (5sin(sqrt(x)))/(sqrt(x))	\int\:\frac{5\sin(\sqrt{x})}{\sqrt{x}}dx
y^'-2/t y=t^3	y^{\prime\:}-\frac{2}{t}y=t^{3}
laplacetransform tcos(pit)	laplacetransform\:t\cdot\:\cos(π\cdot\:t)
laplacetransform e^{-3t}*sin(t)	laplacetransform\:e^{-3t}\cdot\:\sin(t)
derivative of sin(5x^5)	\frac{d}{dx}(\sin(5)x^{5})
derivative of x^{4sin(x})	\frac{d}{dx}(x^{4\sin(x)})
ydx+x(ln(x)-ln(y)-1)dy=0,y(1)=e	ydx+x(\ln(x)-\ln(y)-1)dy=0,y(1)=e
derivative of sqrt(4t^2-t)	derivative\:\sqrt{4t^{2}-t}
limit as x approaches 0 of (1-sqrt(x))/(1-x)	\lim\:_{x\to\:0}(\frac{1-\sqrt{x}}{1-x})
sum from n=0 to infinity of 1/(9^n)	\sum\:_{n=0}^{\infty\:}\frac{1}{9^{n}}
limit as x approaches 0 of (-2-2cos(x)+2)/(x^4)	\lim\:_{x\to\:0}(\frac{-2-2\cos(x)+2}{x^{4}})
derivative of f(x)=14sqrt(x)	derivative\:f(x)=14\sqrt{x}
derivative of y=tan^2(8x)	derivative\:y=\tan^{2}(8x)
integral of 42x(x+1)^5	\int\:42x(x+1)^{5}dx
integral of 1/(2x^2+5)	\int\:\frac{1}{2x^{2}+5}dx
integral of sqrt(tan(4x))sec^2(4x)	\int\:\sqrt{\tan(4x)}\sec^{2}(4x)dx
integral of 15x*sqrt(1-x)	\int\:15x\cdot\:\sqrt{1-x}dx
derivative of (4-sec(x))/(tan(x))	derivative\:\frac{4-\sec(x)}{\tan(x)}
limit as x approaches 0 of 1/(ln(1+x))-1/x	\lim\:_{x\to\:0}(\frac{1}{\ln(1+x)}-\frac{1}{x})
derivative of (x^4+3x)^{-1}	derivative\:(x^{4}+3x)^{-1}
derivative of x^2+(3456/x)	\frac{d}{dx}(x^{2}+\frac{3456}{x})
inverse oflaplace 1/(s(s^2+81))	inverselaplace\:\frac{1}{s(s^{2}+81)}
derivative of (dy/(dx))+81y=0	\frac{d}{dx}(\frac{dy}{dx})+81y=0
integral of cos(u/v)	\int\:\cos(\frac{u}{v})du
limit as x approaches+0 of (sin(0))/0	\lim\:_{x\to\:+0}(\frac{\sin(0)}{0})
laplacetransform 4e^{((2t)/3)}	laplacetransform\:4e^{(\frac{2t}{3})}
integral of 1/(x^3sqrt(x^2-25))	\int\:\frac{1}{x^{3}\sqrt{x^{2}-25}}dx
derivative of (sqrt(t))/(2t-3)	derivative\:\frac{\sqrt{t}}{2t-3}
integral of x(x^2)	\int\:x(x^{2})dx
area f(x)=16-x^2,0,4	area\:f(x)=16-x^{2},0,4
integral of 1/(xsqrt(64x^2-5))	\int\:\frac{1}{x\sqrt{64x^{2}-5}}dx
integral of (3x^3)/(4+x^8)	\int\:\frac{3x^{3}}{4+x^{8}}dx
y^{''}-3y^'+2y=e^{3x}(x+1)	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=e^{3x}(x+1)
tangent of f(x)=9x-8sqrt(x),(1,1)	tangent\:f(x)=9x-8\sqrt{x},(1,1)
integral of (e^{3x})/(e^{3x)-e^{-3x}}	\int\:\frac{e^{3x}}{e^{3x}-e^{-3x}}dx
limit as x approaches-6 of (-9x)/(x+6)	\lim\:_{x\to\:-6}(\frac{-9x}{x+6})
integral of 9sec^3(x)	\int\:9\sec^{3}(x)dx
(d^2)/(dx^2)(sqrt(1-x^2))	\frac{d^{2}}{dx^{2}}(\sqrt{1-x^{2}})
integral of 23e^x	\int\:23e^{x}dx
integral of (sin(2x))/(13+cos^2(x))	\int\:\frac{\sin(2x)}{13+\cos^{2}(x)}dx
area y=4x,x=4,y= 4/x ,x=0	area\:y=4x,x=4,y=\frac{4}{x},x=0
(\partial)/(\partial x)(ln(3ye^{xy}))	\frac{\partial\:}{\partial\:x}(\ln(3ye^{xy}))
inverse oflaplace ((s+1)^3)/(s^6)	inverselaplace\:\frac{(s+1)^{3}}{s^{6}}
integral of 1/((3+y)^5)	\int\:\frac{1}{(3+y)^{5}}dy
simplify (x^2)/(sqrt(x-1))	simplify\:\frac{x^{2}}{\sqrt{x-1}}
integral of-(1300)/(x^2)	\int\:-\frac{1300}{x^{2}}dx
derivative of (3x/x)	\frac{d}{dx}(\frac{3x}{x})
tangent of f(x)=(sqrt(2))^x,\at x=6	tangent\:f(x)=(\sqrt{2})^{x},\at\:x=6
y^{''}+14y^'+28y=6675e^{2t}cos(15t)	y^{\prime\:\prime\:}+14y^{\prime\:}+28y=6675e^{2t}\cos(15t)
laplacetransform t^2sin(t)	laplacetransform\:t^{2}\sin(t)
derivative of (1+5t)/(ln(t^2))	derivative\:\frac{1+5t}{\ln(t^{2})}
integral of (x^2)/(sqrt(x^6-1))	\int\:\frac{x^{2}}{\sqrt{x^{6}-1}}dx
integral from 1 to 10 of 5x^{-2}	\int\:_{1}^{10}5x^{-2}dx
f(x)= 1/(x^7)	f(x)=\frac{1}{x^{7}}
integral of (sec^4(x))/(sqrt(tan(x)))	\int\:\frac{\sec^{4}(x)}{\sqrt{\tan(x)}}dx
(\partial)/(\partial y)(7xsin(9x^2y))	\frac{\partial\:}{\partial\:y}(7x\sin(9x^{2}y))
limit as x approaches-infinity of xe^{-x+2}	\lim\:_{x\to\:-\infty\:}(xe^{-x+2})
(\partial)/(\partial x)(ln(x+3y+4z))	\frac{\partial\:}{\partial\:x}(\ln(x+3y+4z))
integral of (x^2)/((3x+1)^3)	\int\:\frac{x^{2}}{(3x+1)^{3}}dx
derivative of (5x^{1/2})	\frac{d}{dx}((5x)^{\frac{1}{2}})
derivative of xcos(pix+1)	\frac{d}{dx}(x\cos(πx)+1)
y^{'''}-3y^{''}+3y^'-y=0	y^{\prime\:\prime\:\prime\:}-3y^{\prime\:\prime\:}+3y^{\prime\:}-y=0
limit as x approaches 4+of 2/(x^2-16)	\lim\:_{x\to\:4+}(\frac{2}{x^{2}-16})
limit as x approaches infinity of x^{3x}	\lim\:_{x\to\:\infty\:}(x^{3x})
derivative of f(x)= 3/(8x)	derivative\:f(x)=\frac{3}{8x}
derivative of e^x(sin(x-cos(x)))	\frac{d}{dx}(e^{x}(\sin(x)-\cos(x)))
area x^2,12-x,-4,3	area\:x^{2},12-x,-4,3
integral of (-x^4+1)^2(-4x^3)	\int\:(-x^{4}+1)^{2}(-4x^{3})dx
derivative of (8x^3-6/(x^2))	\frac{d}{dx}(\frac{8x^{3}-6}{x^{2}})
y^'=-sqrt(x)	y^{\prime\:}=-\sqrt{x}
derivative of y=((x^2+6)/(x^2-6))^3	derivative\:y=(\frac{x^{2}+6}{x^{2}-6})^{3}
derivative of arcsin(3x+arccos(3x))	\frac{d}{dx}(\arcsin(3x)+\arccos(3x))
derivative of arccot(x/8)	\frac{d}{dx}(\arccot(\frac{x}{8}))
limit as x approaches 0 of (1+x)^{3/x}	\lim\:_{x\to\:0}((1+x)^{\frac{3}{x}})
y^{''}-5/t y^'+(18)/(t^2)y=0	y^{\prime\:\prime\:}-\frac{5}{t}y^{\prime\:}+\frac{18}{t^{2}}y=0

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