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Popular Calculus Problems

derivative of (x^2+1)^3(2x^3-5x)^2	derivative\:(x^{2}+1)^{3}(2x^{3}-5x)^{2}
derivative of (1+x/(sqrt(x)))	\frac{d}{dx}(\frac{1+x}{\sqrt{x}})
integral of (2x-3)/(sqrt(1-x^2))	\int\:\frac{2x-3}{\sqrt{1-x^{2}}}dx
y^{''}+y-2*cos(x)=0	y^{\prime\:\prime\:}+y-2\cdot\:\cos(x)=0
derivative of ln(t^2-2t+10)	derivative\:\ln(t^{2}-2t+10)
area 1/x ,x^2,[1,e]	area\:\frac{1}{x},x^{2},[1,e]
integral of (5x)/((x-1)^3)	\int\:\frac{5x}{(x-1)^{3}}dx
(\partial)/(\partial x)(y^5sin(4x))	\frac{\partial\:}{\partial\:x}(y^{5}\sin(4x))
y(x+7)+y^'=0,y(-14)=1	y(x+7)+y^{\prime\:}=0,y(-14)=1
derivative of 7cos(7x)	\frac{d}{dx}(7\cos(7x))
integral from 0 to 2pi of xsin(x)	\int\:_{0}^{2π}x\sin(x)dx
integral of-7x	\int\:-7xdx
limit as x approaches-2+of (x+2)/(x^3+8)	\lim\:_{x\to\:-2+}(\frac{x+2}{x^{3}+8})
derivative of 1/(sqrt(x-9))	derivative\:\frac{1}{\sqrt{x-9}}
(\partial)/(\partial y)(x^5+xy^7+4)	\frac{\partial\:}{\partial\:y}(x^{5}+xy^{7}+4)
y^'=((3y^2-x^2))/(2xy)	y^{\prime\:}=\frac{(3y^{2}-x^{2})}{2xy}
derivative of 2xlog_{6}(sqrt(x))	\frac{d}{dx}(2x\log_{6}(\sqrt{x}))
derivative of 8xsin(pix)	\frac{d}{dx}(8x\sin(πx))
d/(dy)(y^4)	\frac{d}{dy}(y^{4})
integral of (3x^3+2)/(x^2sqrt(x^2-4))	\int\:\frac{3x^{3}+2}{x^{2}\sqrt{x^{2}-4}}dx
(d^3)/(dx^3)(3/x)	\frac{d^{3}}{dx^{3}}(\frac{3}{x})
integral of sin(2x+5)	\int\:\sin(2x+5)dx
derivative of f(x)=arctan((x-1)/(x+1))	derivative\:f(x)=\arctan(\frac{x-1}{x+1})
normal of y=sqrt(x),\at x=4	normal\:y=\sqrt{x},\at\:x=4
tangent of f(x)=9-x^2,\at x=-1	tangent\:f(x)=9-x^{2},\at\:x=-1
derivative of x^{-2/3}	derivative\:x^{-\frac{2}{3}}
integral of (7x+6)/(x^2(x+2))	\int\:\frac{7x+6}{x^{2}(x+2)}dx
tangent of y=8x^2+8,(2,40)	tangent\:y=8x^{2}+8,(2,40)
(\partial)/(\partial z)(xe^{y-z^2})	\frac{\partial\:}{\partial\:z}(xe^{y-z^{2}})
derivative of 5x+x^2	\frac{d}{dx}(5x+x^{2})
limit as x approaches 5+of 5sqrt(x-5)	\lim\:_{x\to\:5+}(5\sqrt{x-5})
(\partial)/(\partial t)(t^2e^{-x})	\frac{\partial\:}{\partial\:t}(t^{2}e^{-x})
inverse oflaplace 1/(s^2+s+1)*1/s	inverselaplace\:\frac{1}{s^{2}+s+1}\cdot\:\frac{1}{s}
derivative of sqrt(1-5x)	\frac{d}{dx}(\sqrt{1-5x})
(d^3)/(dx^3)(1/(1+x^2))	\frac{d^{3}}{dx^{3}}(\frac{1}{1+x^{2}})
(dy)/(dx)= 1/(x(ln(2)))	\frac{dy}{dx}=\frac{1}{x(\ln(2))}
derivative of f(x)=(b/(a+z^2))^7	derivative\:f(x)=(\frac{b}{a+z^{2}})^{7}
integral of ((2x+3))/(x+2)	\int\:\frac{(2x+3)}{x+2}dx
sum from n=1 to infinity of (5n)/(2n+5)	\sum\:_{n=1}^{\infty\:}\frac{5n}{2n+5}
derivative of (sqrt(25-x^2)/(4x))	\frac{d}{dx}(\frac{\sqrt{25-x^{2}}}{4x})
(\partial)/(\partial x)(-12xy)	\frac{\partial\:}{\partial\:x}(-12xy)
xy^'-3y=0	xy^{\prime\:}-3y=0
derivative of y((x-y)/(x+y))	derivative\:y(\frac{x-y}{x+y})
integral of 1/(sqrt(16x^2+2))	\int\:\frac{1}{\sqrt{16x^{2}+2}}dx
derivative of 5x+9	\frac{d}{dx}(5x+9)
derivative of cosh(x)	\frac{d}{dx}(\cosh(x))
integral of 1/(y^2sqrt(y^2+25))	\int\:\frac{1}{y^{2}\sqrt{y^{2}+25}}dy
derivative of 7cos^2(x)	\frac{d}{dx}(7\cos^{2}(x))
f^{''}(x)=2,f^'(2)=5,f(2)=10	f^{\prime\:\prime\:}(x)=2,f^{\prime\:}(2)=5,f(2)=10
d/(dθ)(cos(2θ)+isin(2θ))	\frac{d}{dθ}(\cos(2θ)+i\sin(2θ))
derivative of (3x-x^2(3-x-x^2))	\frac{d}{dx}((3x-x^{2})(3-x-x^{2}))
integral of (x^2+84x+84)/(x^3-4x)	\int\:\frac{x^{2}+84x+84}{x^{3}-4x}dx
(\partial)/(\partial x)(3x^4+5x^4+9xy)	\frac{\partial\:}{\partial\:x}(3x^{4}+5x^{4}+9xy)
(\partial)/(\partial s)(7/s)	\frac{\partial\:}{\partial\:s}(\frac{7}{s})
derivative of h(x)=x^3+4x^4	derivative\:h(x)=x^{3}+4x^{4}
derivative of f(t)=sin(2t)	derivative\:f(t)=\sin(2t)
derivative of y=\sqrt[3]{1+4x}	derivative\:y=\sqrt[3]{1+4x}
derivative of 0.04t^3-0.12t^2	derivative\:0.04t^{3}-0.12t^{2}
limit as x approaches 3-of (x+2)/(x^2-9)	\lim\:_{x\to\:3-}(\frac{x+2}{x^{2}-9})
derivative of sqrt(x+8)	derivative\:\sqrt{x+8}
(\partial)/(\partial x)(e^{x/y})	\frac{\partial\:}{\partial\:x}(e^{\frac{x}{y}})
(\partial)/(\partial r)(rsin(t)sin(x))	\frac{\partial\:}{\partial\:r}(r\sin(t)\sin(x))
integral from 0 to 1 of (17)/(4y-1)	\int\:_{0}^{1}\frac{17}{4y-1}dy
inverse oflaplace 6/s+8a*s/(s^2+16)	inverselaplace\:\frac{6}{s}+8a\cdot\:\frac{s}{s^{2}+16}
derivative of y=sqrt(x)+\sqrt[5]{x}	derivative\:y=\sqrt{x}+\sqrt[5]{x}
derivative of 4x^4+1/3 x^3+x+1	\frac{d}{dx}(4x^{4}+\frac{1}{3}x^{3}+x+1)
h	h
derivative of (1-sin(x)/(1+sin(x)))	\frac{d}{dx}(\frac{1-\sin(x)}{1+\sin(x)})
integral of e^{ex}	\int\:e^{ex}dx
integral of (x^2+1+1/(x^2+1))	\int\:(x^{2}+1+\frac{1}{x^{2}+1})dx
integral of 5/(x^3)	\int\:\frac{5}{x^{3}}dx
integral of (cos(3x)+3)/(sin(3x))	\int\:\frac{\cos(3x)+3}{\sin(3x)}dx
inverse oflaplace 3/(s(s+3)+6)	inverselaplace\:\frac{3}{s(s+3)+6}
(\partial)/(\partial x)(\|x\|y)	\frac{\partial\:}{\partial\:x}(\left\|x\right\|y)
derivative of (e^{3x}+e^{x^2}/3)	\frac{d}{dx}(\frac{e^{3x}+e^{x^{2}}}{3})
integral of e^{-3x}+2x	\int\:e^{-3x}+2xdx
integral of (-x)/(x^2+4)	\int\:\frac{-x}{x^{2}+4}dx
limit as x approaches 1 of 2x-1	\lim\:_{x\to\:1}(2x-1)
tangent of f(x)=3x-2x^2	tangent\:f(x)=3x-2x^{2}
(dy)/(dx)-y=e^x	\frac{dy}{dx}-y=e^{x}
sum from n=0 to infinity of 9(2/3)^n	\sum\:_{n=0}^{\infty\:}9(\frac{2}{3})^{n}
(dy)/(dt)=9y-y^2-81/4	\frac{dy}{dt}=9y-y^{2}-\frac{81}{4}
d/(da)(sin^4(a)-cos^4(a)+2cos^2(a))	\frac{d}{da}(\sin^{4}(a)-\cos^{4}(a)+2\cos^{2}(a))
integral of (sin(2x))/(1+cos^4(x))	\int\:\frac{\sin(2x)}{1+\cos^{4}(x)}dx
derivative of y=(x+1)/x	derivative\:y=\frac{x+1}{x}
limit as x approaches-87 of F(x)	\lim\:_{x\to\:-87}(F(x))
integral from 0 to 1 of x^4e^{-x}	\int\:_{0}^{1}x^{4}e^{-x}dx
sum from n=0 to infinity of 5*3^n	\sum\:_{n=0}^{\infty\:}5\cdot\:3^{n}
derivative of f(x)=(x^2-1)(x^2+1)	derivative\:f(x)=(x^{2}-1)(x^{2}+1)
sum from n=1 to infinity of (x^n)/(11^n)	\sum\:_{n=1}^{\infty\:}\frac{x^{n}}{11^{n}}
integral of 2(x-2)	\int\:2(x-2)dx
integral of cos(t-x)	\int\:\cos(t-x)dx
derivative of f(x)=7x-5	derivative\:f(x)=7x-5
integral of (2x+4)^2	\int\:(2x+4)^{2}dx
derivative of 1/(ln(2))	\frac{d}{dx}(\frac{1}{\ln(2)})
tangent of y=(7x)/(x-1),(2,14)	tangent\:y=\frac{7x}{x-1},(2,14)
(\partial)/(\partial x)((x+2)^2*(1+1/y)^3)	\frac{\partial\:}{\partial\:x}((x+2)^{2}\cdot\:(1+\frac{1}{y})^{3})
derivative of y=sqrt(x^2+11)	derivative\:y=\sqrt{x^{2}+11}
(\partial)/(\partial z)(x-z)	\frac{\partial\:}{\partial\:z}(x-z)
(\partial)/(\partial x)(x^5y^{-1/2})	\frac{\partial\:}{\partial\:x}(x^{5}y^{-\frac{1}{2}})

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