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Popular Calculus Problems

(\partial)/(\partial x)(y^{x^2-y})	\frac{\partial\:}{\partial\:x}(y^{x^{2}-y})
derivative of 3t-4t^2	derivative\:3t-4t^{2}
(dy)/(dx)y=cos^{-1}(1/x)	\frac{dy}{dx}y=\cos^{-1}(\frac{1}{x})
slope of (3.4)(-6.4)	slope\:(3.4)(-6.4)
limit as x approaches 0-of ln(x^8)	\lim\:_{x\to\:0-}(\ln(x^{8}))
derivative of 8/(x^2+4)	derivative\:\frac{8}{x^{2}+4}
integral of 9xsec(x)tan(x)	\int\:9x\sec(x)\tan(x)dx
y^{''}+y=cos^2(x)	y^{\prime\:\prime\:}+y=\cos^{2}(x)
integral of 3v(v^2+2)^2	\int\:3v(v^{2}+2)^{2}dv
integral of (3xsqrt(1-2x^2))	\int\:(3x\sqrt{1-2x^{2}})dx
area 4x+3,x^3+3	area\:4x+3,x^{3}+3
integral from 0 to infinity of 1/(e^x+1)	\int\:_{0}^{\infty\:}\frac{1}{e^{x}+1}dx
integral of-(\sqrt[3]{x^2})/5	\int\:-\frac{\sqrt[3]{x^{2}}}{5}dx
integral of sqrt((4+x)/(4-x))	\int\:\sqrt{\frac{4+x}{4-x}}dx
(\partial)/(\partial y)(x^4-3x^2y)	\frac{\partial\:}{\partial\:y}(x^{4}-3x^{2}y)
integral of (y^2)/(x^2)	\int\:\frac{y^{2}}{x^{2}}dx
derivative of (8x^5-15)/(x^4)	derivative\:\frac{8x^{5}-15}{x^{4}}
taylor 1/((x^2+1))	taylor\:\frac{1}{(x^{2}+1)}
(dy)/(dx)=8x^3e^{-2y}	\frac{dy}{dx}=8x^{3}e^{-2y}
derivative of (1+tan(2x)^3)	\frac{d}{dx}((1+\tan(2x))^{3})
d/(dt)(te^{5t})	\frac{d}{dt}(te^{5t})
(\partial)/(\partial x)(2x^4y+1)	\frac{\partial\:}{\partial\:x}(2x^{4}y+1)
integral from 1 to 2 of 3^{-x}	\int\:_{1}^{2}3^{-x}dx
integral of (sqrt(x^2-1))	\int\:(\sqrt{x^{2}-1})dx
derivative of (3-x/2)	\frac{d}{dx}(\frac{3-x}{2})
derivative of x^4cos(x)	derivative\:x^{4}\cos(x)
integral of 2t*e^t	\int\:2t\cdot\:e^{t}dt
area y=x^2-1.521,y=-x^2+1.521	area\:y=x^{2}-1.521,y=-x^{2}+1.521
limit as x approaches 0-of 2^{1/x}+2	\lim\:_{x\to\:0-}(2^{\frac{1}{x}}+2)
inverse oflaplace (e^{-s})/s	inverselaplace\:\frac{e^{-s}}{s}
(1+e^x)y(dy)/(dx)=e^y	(1+e^{x})y\frac{dy}{dx}=e^{y}
8x(dy)/(dx)=2xe^x-8y+6x^2	8x\frac{dy}{dx}=2xe^{x}-8y+6x^{2}
derivative of (sec(9x))/(1+sec(9x))	derivative\:\frac{\sec(9x)}{1+\sec(9x)}
(\partial)/(\partial x)((-x-9y)/(2y-7x))	\frac{\partial\:}{\partial\:x}(\frac{-x-9y}{2y-7x})
derivative of 3sin(x-4sin^3(x))	\frac{d}{dx}(3\sin(x)-4\sin^{3}(x))
limit as x approaches 0+of 1/(1-e^x)-1/x	\lim\:_{x\to\:0+}(\frac{1}{1-e^{x}}-\frac{1}{x})
derivative of 1/(x^2+1/x)	\frac{d}{dx}(\frac{1}{x^{2}}+\frac{1}{x})
integral of 6sin^2(x)cos^2(x)	\int\:6\sin^{2}(x)\cos^{2}(x)dx
sum from n=1 to infinity of 3/(2sqrt(n))	\sum\:_{n=1}^{\infty\:}\frac{3}{2\sqrt{n}}
(\partial)/(\partial x)(e^{x+2y})	\frac{\partial\:}{\partial\:x}(e^{x+2y})
(ln(x^2+8x+21))^'	(\ln(x^{2}+8x+21))^{\prime\:}
derivative of (2x^{-3x})	\frac{d}{dx}((2x)^{-3x})
integral of ((x^3-2x^2-4))/((x^3-2x^2))	\int\:\frac{(x^{3}-2x^{2}-4)}{(x^{3}-2x^{2})}dx
integral of (x^4)/4	\int\:\frac{x^{4}}{4}dx
(dy)/(dx)=y(xy^5-1)	\frac{dy}{dx}=y(xy^{5}-1)
xy^'+y=0	xy^{\prime\:}+y=0
(d^2)/(dx^2)(\sqrt[5]{x})	\frac{d^{2}}{dx^{2}}(\sqrt[5]{x})
derivative of arccos(x)+x	derivative\:\arccos(x)+x
integral of 1/((3sin(x)-4cos(x)))	\int\:\frac{1}{(3\sin(x)-4\cos(x))}dx
d/(dn)(ln(n+1))	\frac{d}{dn}(\ln(n+1))
integral of 6/((x-4)^3)	\int\:\frac{6}{(x-4)^{3}}dx
(\partial)/(\partial x)(3x^2y+6xy^3)	\frac{\partial\:}{\partial\:x}(3x^{2}y+6xy^{3})
sum from n=2 to infinity of e^{1/n}	\sum\:_{n=2}^{\infty\:}e^{\frac{1}{n}}
derivative of e^{-3x}cos(3x)	\frac{d}{dx}(e^{-3x}\cos(3x))
derivative of (14+5x-3x^2^{3/4})	\frac{d}{dx}((14+5x-3x^{2})^{\frac{3}{4}})
derivative of x^2sin^8(x+xcos^{-6}(x))	\frac{d}{dx}(x^{2}\sin^{8}(x)+x\cos^{-6}(x))
integral from 0 to 2pi of 6x^2sin(x/4)	\int\:_{0}^{2π}6x^{2}\sin(\frac{x}{4})dx
(\partial)/(\partial x)(e^{xyz}tan(x+2y+z))	\frac{\partial\:}{\partial\:x}(e^{xyz}\tan(x+2y+z))
derivative of xsin(2/x)	derivative\:x\sin(\frac{2}{x})
area y=4x^3+x,x=2,x=-1,x	area\:y=4x^{3}+x,x=2,x=-1,x
limit as x approaches-2 of (x-1)/(x+2)	\lim\:_{x\to\:-2}(\frac{x-1}{x+2})
simplify 1/(y^2)-3/(y^4)	simplify\:\frac{1}{y^{2}}-\frac{3}{y^{4}}
integral of (3x)/(sqrt(4-x))	\int\:\frac{3x}{\sqrt{4-x}}dx
inverse oflaplace (10)/(s(s+1)(s+10))	inverselaplace\:\frac{10}{s(s+1)(s+10)}
slope of (-1,-2),(5,4)	slope\:(-1,-2),(5,4)
y(dy)/(dx)=xe^{-y^2}	y\frac{dy}{dx}=xe^{-y^{2}}
tangent of (5x)/(x-2)	tangent\:\frac{5x}{x-2}
integral of ((x^2-x+12))/(x^3+2x)	\int\:\frac{(x^{2}-x+12)}{x^{3}+2x}dx
integral from 0 to infinity of e^{-u}	\int\:_{0}^{\infty\:}e^{-u}du
(dy)/(dx)=y^2-3y	\frac{dy}{dx}=y^{2}-3y
limit as t approaches 0 of ((3e^t-3))/t	\lim\:_{t\to\:0}(\frac{(3e^{t}-3)}{t})
derivative of-(2x/((x^2+3)^2))	\frac{d}{dx}(-\frac{2x}{(x^{2}+3)^{2}})
limit as x approaches 0+of (8x)/(sin(x))	\lim\:_{x\to\:0+}(\frac{8x}{\sin(x)})
limit as x approaches-3 of \|x+3\|	\lim\:_{x\to\:-3}(\left\|x+3\right\|)
limit as x approaches 0-of e^{1/x}+1	\lim\:_{x\to\:0-}(e^{\frac{1}{x}}+1)
derivative of (1/(y^2)-6/(y^4))(y+4y^3)	derivative\:(\frac{1}{y^{2}}-\frac{6}{y^{4}})(y+4y^{3})
limit as x approaches 3 of In(x-3)	\lim\:_{x\to\:3}(In(x-3))
derivative of (f(x))^3	derivative\:(f(x))^{3}
area y=x^2+1,(-1,2)	area\:y=x^{2}+1,(-1,2)
integral of u^3sqrt(u^4+2)	\int\:u^{3}\sqrt{u^{4}+2}du
derivative of e^{-x}ln(x)	\frac{d}{dx}(e^{-x}\ln(x))
integral from 0 to 1 of-x^2+4x+1	\int\:_{0}^{1}-x^{2}+4x+1dx
integral of 1/(7x+4)	\int\:\frac{1}{7x+4}dx
implicit (dy)/(dx),xy-6=0	implicit\:\frac{dy}{dx},xy-6=0
integral of 2sin^3(5x)cos^3(5x)	\int\:2\sin^{3}(5x)\cos^{3}(5x)dx
derivative of \sqrt[3]{x^2+1}	\frac{d}{dx}(\sqrt[3]{x^{2}+1})
(\partial)/(\partial x)(sin^3(x^2y))	\frac{\partial\:}{\partial\:x}(\sin^{3}(x^{2}y))
(dy)/(dx)+3yx^3=0	\frac{dy}{dx}+3yx^{3}=0
integral of t^2sin(nt)	\int\:t^{2}\sin(nt)dt
limit as x approaches e+of (ln(x))^{1/(x-e)}	\lim\:_{x\to\:e+}((\ln(x))^{\frac{1}{x-e}})
y^{''}+9y=e^t(cos(3t)+sin(3t))	y^{\prime\:\prime\:}+9y=e^{t}(\cos(3t)+\sin(3t))
limit as x approaches 9 of 7x+\|x-9\|	\lim\:_{x\to\:9}(7x+\left\|x-9\right\|)
derivative of f(x)=(x^3)/4-3x	derivative\:f(x)=\frac{x^{3}}{4}-3x
(\partial)/(\partial x)(y^3cos(3x)*3)	\frac{\partial\:}{\partial\:x}(y^{3}\cos(3x)\cdot\:3)
derivative of e^x+e^{-x}-2	\frac{d}{dx}(e^{x}+e^{-x}-2)
integral from 0 to 2 of (2t)/((t-3)^2)	\int\:_{0}^{2}\frac{2t}{(t-3)^{2}}dt
(\partial)/(\partial x)((9x-2y)/(9x+2y))	\frac{\partial\:}{\partial\:x}(\frac{9x-2y}{9x+2y})
derivative of f(x)=(x^{1/3}-4)/(x^{7/2)}	derivative\:f(x)=\frac{x^{\frac{1}{3}}-4}{x^{\frac{7}{2}}}
derivative of c*sin((pix)/L)	derivative\:c\cdot\:\sin(\frac{πx}{L})
derivative of (sqrt(3))/4 s^2	derivative\:\frac{\sqrt{3}}{4}s^{2}

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