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Popular Calculus Problems

derivative of cos^2(x-sin^2(x))	\frac{d}{dx}(\cos^{2}(x)-\sin^{2}(x))
y^'+y/x =2x^4y^2	y^{\prime\:}+\frac{y}{x}=2x^{4}y^{2}
derivative of e^{cos(4x})	\frac{d}{dx}(e^{\cos(4x)})
slope of (6.3)(7.8)	slope\:(6.3)(7.8)
tangent of 33x^3	tangent\:33x^{3}
integral of (a+bx^7)/(sqrt(8ax+bx^8))	\int\:\frac{a+bx^{7}}{\sqrt{8ax+bx^{8}}}dx
tangent of f(x)=4e^x+x,\at x=0	tangent\:f(x)=4e^{x}+x,\at\:x=0
derivative of cos((1-e^{7x}/(1+e^{7x)}))	\frac{d}{dx}(\cos(\frac{1-e^{7x}}{1+e^{7x}}))
f(x)=(csc(x))/(1+csc(x))	f(x)=\frac{\csc(x)}{1+\csc(x)}
derivative of f(x)=x^2*e^x	derivative\:f(x)=x^{2}\cdot\:e^{x}
integral from 1 to 4 of 4x^2	\int\:_{1}^{4}4x^{2}dx
integral of e^{sin(x)}	\int\:e^{\sin(x)}dx
derivative of 5xe^{-x}-3e^{x^2}	derivative\:5xe^{-x}-3e^{x^{2}}
limit as x approaches infinity of 10^x	\lim\:_{x\to\:\infty\:}(10^{x})
derivative of (6x)^{5x}	derivative\:(6x)^{5x}
d/(dy)(-x^2y^2sin(x)+2xy^2cos(x))	\frac{d}{dy}(-x^{2}y^{2}\sin(x)+2xy^{2}\cos(x))
integral of sqrt(x/(1-x))	\int\:\sqrt{\frac{x}{1-x}}dx
y^'=3-y	y^{\prime\:}=3-y
(dy)/(dx)+3x^2y=sin(x)e^{-x^3}	\frac{dy}{dx}+3x^{2}y=\sin(x)e^{-x^{3}}
implicit cos(xy)=1+sin(y)	implicit\:\cos(xy)=1+\sin(y)
derivative of 4e^{3x^2}	\frac{d}{dx}(4e^{3x^{2}})
derivative of (2x^3+5)/(4x^2+7)	derivative\:\frac{2x^{3}+5}{4x^{2}+7}
taylor 1+x^2	taylor\:1+x^{2}
derivative of-1/4 (x^{-4}-x^8)	derivative\:-\frac{1}{4}(x^{-4}-x^{8})
laplacetransform e^{-pi/2 t}	laplacetransform\:e^{-\frac{π}{2}t}
integral of e^{1/2 x^2}*x^3	\int\:e^{\frac{1}{2}x^{2}}\cdot\:x^{3}dx
derivative of (4+x^2^{-1})	\frac{d}{dx}((4+x^{2})^{-1})
integral of (x^8-(2x^5)/7-sqrt(5))	\int\:(x^{8}-\frac{2x^{5}}{7}-\sqrt{5})dx
y^'=(x^2+xy+y^2)/(x^2)	y^{\prime\:}=\frac{x^{2}+xy+y^{2}}{x^{2}}
dy=(x-2xy)dx	dy=(x-2xy)dx
tangent of x^2+4x-8	tangent\:x^{2}+4x-8
limit as x approaches 0+of x^5ln(x)	\lim\:_{x\to\:0+}(x^{5}\ln(x))
limit as x approaches 1-of 6x-2	\lim\:_{x\to\:1-}(6x-2)
(\partial)/(\partial x)(3x^2y^2+x/y)	\frac{\partial\:}{\partial\:x}(3x^{2}y^{2}+\frac{x}{y})
derivative of y=sin(3x+2y)	derivative\:y=\sin(3x+2y)
integral of (5-3x+x^2)	\int\:(5-3x+x^{2})dx
derivative of 1/(5-x)	\frac{d}{dx}(\frac{1}{5-x})
tangent of f(x)=e^{-2x},(0,1)	tangent\:f(x)=e^{-2x},(0,1)
y^{''}-2y^'+10y=e^{-x}	y^{\prime\:\prime\:}-2y^{\prime\:}+10y=e^{-x}
derivative of e^{-x+1}-e^{-x+1}*x	derivative\:e^{-x+1}-e^{-x+1}\cdot\:x
(\partial)/(\partial x)(y*cos(x-y))	\frac{\partial\:}{\partial\:x}(y\cdot\:\cos(x-y))
tangent of 7x-4x^2	tangent\:7x-4x^{2}
integral of-1/(2\sqrt[3]{x^2)}	\int\:-\frac{1}{2\sqrt[3]{x^{2}}}dx
integral of 11ln(\sqrt[3]{x})	\int\:11\ln(\sqrt[3]{x})dx
y^'=y(4-ty)	y^{\prime\:}=y(4-ty)
derivative of cos^2(x+sin^2(x))	\frac{d}{dx}(\cos^{2}(x)+\sin^{2}(x))
derivative of f(x)=(56)/(x^9)	derivative\:f(x)=\frac{56}{x^{9}}
limit as x approaches 0 of x^2-3	\lim\:_{x\to\:0}(x^{2}-3)
limit as x approaches 2 of (x+5)/(x-2)	\lim\:_{x\to\:2}(\frac{x+5}{x-2})
integral of 2sin(x)-1	\int\:2\sin(x)-1dx
derivative of sin^5(sqrt(ln(e^{3x-1)}))	\frac{d}{dx}(\sin^{5}(\sqrt{\ln(e^{3x-1})}))
integral of te^{-t}-2	\int\:te^{-t}-2dt
integral of 2sqrt(x)+6cos(x)	\int\:2\sqrt{x}+6\cos(x)dx
integral of (25-x^2)^{1/2}	\int\:(25-x^{2})^{\frac{1}{2}}dx
derivative of 1/(e^x-1)	\frac{d}{dx}(\frac{1}{e^{x}-1})
integral of x^5+2x^3+x	\int\:x^{5}+2x^{3}+xdx
derivative of x+60	\frac{d}{dx}(x+60)
integral from 0 to infinity of 1/(x^5)	\int\:_{0}^{\infty\:}\frac{1}{x^{5}}dx
integral of ye^{x/y}	\int\:ye^{\frac{x}{y}}dx
integral of x/(sqrt(12-9x^2))	\int\:\frac{x}{\sqrt{12-9x^{2}}}dx
integral from 1 to 4 of sqrt(x)(2+x)	\int\:_{1}^{4}\sqrt{x}(2+x)dx
limit as w approaches 0 of (w^2)/(cos(w)-1)	\lim\:_{w\to\:0}(\frac{w^{2}}{\cos(w)-1})
derivative of 2nde^{2e^x}	derivative\:2nde^{2e^{x}}
sum from n=1 to infinity of (n^2)/3	\sum\:_{n=1}^{\infty\:}\frac{n^{2}}{3}
slope ofintercept (3)(6.9)	slopeintercept\:(3)(6.9)
derivative of (x+6^2)	\frac{d}{dx}((x+6)^{2})
limit as x approaches 0 of (sin(k)x)/x	\lim\:_{x\to\:0}(\frac{\sin(k)x}{x})
tangent of \sqrt[4]{x}	tangent\:\sqrt[4]{x}
integral of (e^x)/(e^4-1)	\int\:\frac{e^{x}}{e^{4}-1}dx
(dy)/(dx)=8y,y(0)=6	\frac{dy}{dx}=8y,y(0)=6
integral of (x^2-29x+5)/((x-4)^2(x^2+3))	\int\:\frac{x^{2}-29x+5}{(x-4)^{2}(x^{2}+3)}dx
integral from 0 to 4 of sqrt(1+9x)	\int\:_{0}^{4}\sqrt{1+9x}dx
maclaurin ln(1-3y)	maclaurin\:\ln(1-3y)
integral of ycos(y^2)	\int\:y\cos(y^{2})dy
derivative of (x*sin(x)/(1+x^2))	\frac{d}{dx}(\frac{x\cdot\:\sin(x)}{1+x^{2}})
integral from 0 to pi of 1-cos^2(x)	\int\:_{0}^{π}1-\cos^{2}(x)dx
derivative of 8e^{pix}+2e^{7x}	\frac{d}{dx}(8e^{πx}+2e^{7x})
(\partial)/(\partial x)(xcos(y)-ye^x)	\frac{\partial\:}{\partial\:x}(x\cos(y)-ye^{x})
sum from n=1 to infinity of 5/n	\sum\:_{n=1}^{\infty\:}\frac{5}{n}
integral of ex^2	\int\:ex^{2}dx
derivative of e^{t/9}cos(t/9)	derivative\:e^{\frac{t}{9}}\cos(\frac{t}{9})
integral of (8x+1)/(x^2+1)	\int\:\frac{8x+1}{x^{2}+1}dx
tangent of f(x)= 8/x ,\at x=5	tangent\:f(x)=\frac{8}{x},\at\:x=5
y^{''}+y=9sin(x)	y^{\prime\:\prime\:}+y=9\sin(x)
derivative of 40ln(3x+1)-x/3	derivative\:40\ln(3x+1)-\frac{x}{3}
integral of 3x-5	\int\:3x-5dx
integral of 1/(13-5cos(x))	\int\:\frac{1}{13-5\cos(x)}dx
integral of (xsqrt(x^2+5))	\int\:(x\sqrt{x^{2}+5})dx
integral of ye^y-ye	\int\:ye^{y}-yedy
y^{''}+4y=csc^2(2t)	y^{\prime\:\prime\:}+4y=\csc^{2}(2t)
integral of 14sin^2(x)cos^2(x)	\int\:14\sin^{2}(x)\cos^{2}(x)dx
limit as n approaches infinity of \sqrt[n]{cos((npi)/2)}	\lim\:_{n\to\:\infty\:}(\sqrt[n]{\cos(\frac{nπ}{2})})
limit as x approaches 0 of sqrt(0)	\lim\:_{x\to\:0}(\sqrt{0})
integral of sin(x)*cos^3(x)	\int\:\sin(x)\cdot\:\cos^{3}(x)dx
f(x)=8sqrt(x)sin(x)	f(x)=8\sqrt{x}\sin(x)
limit as x approaches 0 of ln(x)*ln(1-x)	\lim\:_{x\to\:0}(\ln(x)\cdot\:\ln(1-x))
integral of (x^2-8)^4(2x)	\int\:(x^{2}-8)^{4}(2x)dx
(\partial)/(\partial x)((6x-7y)/(6x+7y))	\frac{\partial\:}{\partial\:x}(\frac{6x-7y}{6x+7y})
derivative of y=2(1.1)^t	derivative\:y=2(1.1)^{t}
tangent of y=12sqrt(x),(9,36)	tangent\:y=12\sqrt{x},(9,36)

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