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Popular Calculus Problems

derivative of log_{10}(x^3)	\frac{d}{dx}(\log_{10}(x^{3}))
tangent of y=x^3-15x,(2,-22)	tangent\:y=x^{3}-15x,(2,-22)
tangent of 9+5x^2-2x^3	tangent\:9+5x^{2}-2x^{3}
integral of (sqrt(x^2-1))/(x^4)	\int\:\frac{\sqrt{x^{2}-1}}{x^{4}}dx
16y^{''}+7y=0	16y^{\prime\:\prime\:}+7y=0
derivative of 1-e^x+(e-1sin((pi/2)x))	\frac{d}{dx}(1-e^{x}+(e-1)\sin((\frac{π}{2})x))
y^{''}+2y^'+y=2e-t	y^{\prime\:\prime\:}+2y^{\prime\:}+y=2e-t
limit as x approaches 0+of (x^2)/8-6/x	\lim\:_{x\to\:0+}(\frac{x^{2}}{8}-\frac{6}{x})
(\partial)/(\partial x)(sin(ln(x)))	\frac{\partial\:}{\partial\:x}(\sin(\ln(x)))
(\partial)/(\partial y)(x^{-7}y^2+xy^2+3xy)	\frac{\partial\:}{\partial\:y}(x^{-7}y^{2}+xy^{2}+3xy)
(dy)/(dx)=-10y,y(0)=5	\frac{dy}{dx}=-10y,y(0)=5
integral from 0 to 1/2 of 8x(1/2-x)	\int\:_{0}^{\frac{1}{2}}8x(\frac{1}{2}-x)dx
(\partial)/(\partial x)(x*sin(x)-1)	\frac{\partial\:}{\partial\:x}(x\cdot\:\sin(x)-1)
sum from n=1 to infinity of ne^{-n/2}	\sum\:_{n=1}^{\infty\:}ne^{-\frac{n}{2}}
integral of (4x+2)/(x^2)	\int\:\frac{4x+2}{x^{2}}dx
derivative of arccot(e^x)	\frac{d}{dx}(\arccot(e^{x}))
integral of (3x^2)/(x^2-1)	\int\:\frac{3x^{2}}{x^{2}-1}dx
derivative of-3asin(3x+3bcos(3x))	\frac{d}{dx}(-3a\sin(3x)+3b\cos(3x))
limit as x approaches 5+of (2x)/(x-5)	\lim\:_{x\to\:5+}(\frac{2x}{x-5})
simplify 2((2400)/x)	simplify\:2(\frac{2400}{x})
derivative of 8xy-(1/4 (x+y)^4)	\frac{d}{dx}(8xy-(\frac{1}{4})(x+y)^{4})
x(1+y^2)dx=y(1+x^2)dy	x(1+y^{2})dx=y(1+x^{2})dy
slope of (-2,-7),(3,5)	slope\:(-2,-7),(3,5)
y^'= y/(x^2+1)	y^{\prime\:}=\frac{y}{x^{2}+1}
y^{''}-3y^'=x^3-6	y^{\prime\:\prime\:}-3y^{\prime\:}=x^{3}-6
derivative of 15cos(3x)	\frac{d}{dx}(15\cos(3x))
derivative of sqrt(x^4-1)	\frac{d}{dx}(\sqrt{x^{4}-1})
derivative of (3x/(x-2))	\frac{d}{dx}(\frac{3x}{x-2})
integral of 1/(16e^{-4x)+e^{4x}}	\int\:\frac{1}{16e^{-4x}+e^{4x}}dx
derivative of sin((pix)^4)	derivative\:\sin((πx)^{4})
integral from 2 to 4 of (x^2+2)^3x	\int\:_{2}^{4}(x^{2}+2)^{3}xdx
integral of (a-x)^3	\int\:(a-x)^{3}dx
integral of (3+0.5t)	\int\:(3+0.5t)dt
(\partial)/(\partial x)(ln(2x)+5y^3)	\frac{\partial\:}{\partial\:x}(\ln(2x)+5y^{3})
(\partial)/(\partial y)(ln(x+y/(2x)))	\frac{\partial\:}{\partial\:y}(\ln(x+\frac{y}{2x}))
integral from 0 to 1 of 1/(x^{1/2)}	\int\:_{0}^{1}\frac{1}{x^{\frac{1}{2}}}dx
y^'=-10y	y^{\prime\:}=-10y
integral from 0 to infinity of e^{ax}	\int\:_{0}^{\infty\:}e^{ax}dx
(\partial)/(\partial y)(xln(5x+8y))	\frac{\partial\:}{\partial\:y}(x\ln(5x+8y))
derivative of (x^2)/(x+4)	derivative\:\frac{x^{2}}{x+4}
tangent of f(x)=3x^2-2x,\at x=-1	tangent\:f(x)=3x^{2}-2x,\at\:x=-1
d/(dt)(0.9^t)	\frac{d}{dt}(0.9^{t})
limit as x approaches 0 of (x-9)/(x-1)	\lim\:_{x\to\:0}(\frac{x-9}{x-1})
(dy)/(dt)= 1/y	\frac{dy}{dt}=\frac{1}{y}
sum from n=0 to infinity of (-2/3 x)^n	\sum\:_{n=0}^{\infty\:}(-\frac{2}{3}x)^{n}
derivative of 1/(2sqrt(x)+1/(3x^{2/3)})	\frac{d}{dx}(\frac{1}{2\sqrt{x}}+\frac{1}{3x^{\frac{2}{3}}})
(\partial)/(\partial x)(-3xe^{xy})	\frac{\partial\:}{\partial\:x}(-3xe^{xy})
((2sin(x))/(1-2cos(x)))^'	(\frac{2\sin(x)}{1-2\cos(x)})^{\prime\:}
limit as x approaches 0-of 9/x-9/(\|x\|)	\lim\:_{x\to\:0-}(\frac{9}{x}-\frac{9}{\left\|x\right\|})
derivative of x^2(x^3+4)(x^5-6)	derivative\:x^{2}(x^{3}+4)(x^{5}-6)
derivative of x^{3/2}(w+ce^w)	derivative\:x^{\frac{3}{2}}(w+ce^{w})
derivative of 9^xx^{4x}(x^2+2x^2)	\frac{d}{dx}(9^{x}x^{4x}(x^{2}+2x)^{2})
d/(dt)(5e^tsin(t))	\frac{d}{dt}(5e^{t}\sin(t))
derivative of 5x^4-28x^3+42x^2-196x+49	derivative\:5x^{4}-28x^{3}+42x^{2}-196x+49
limit as x approaches 0 of tan^4(4x)	\lim\:_{x\to\:0}(\tan^{4}(4x))
normal of y=5x^3-3x,(1,2)	normal\:y=5x^{3}-3x,(1,2)
limit as x approaches a of 3x^2-2	\lim\:_{x\to\:a}(3x^{2}-2)
limit as x approaches infinity of 24x^7e^{-x^8},[0,x]	\lim\:_{x\to\:\infty\:}(24x^{7}e^{-x^{8}},[0,x])
(\partial)/(\partial y)(xe^{3xy})	\frac{\partial\:}{\partial\:y}(xe^{3xy})
inverse oflaplace s/(s^2+4s-5)	inverselaplace\:\frac{s}{s^{2}+4s-5}
derivative of x^2(3x^2-x-14)	derivative\:x^{2}(3x^{2}-x-14)
integral of x/(6x^2+4)	\int\:\frac{x}{6x^{2}+4}dx
inverse oflaplace ((s-5))/(s(s+4)^2)	inverselaplace\:\frac{(s-5)}{s(s+4)^{2}}
area y=x^2-4x+3,x-y-1=0	area\:y=x^{2}-4x+3,x-y-1=0
integral of (2x^3+6e^x)	\int\:(2x^{3}+6e^{x})dx
integral of (x^2+1)/((x+1)^2)	\int\:\frac{x^{2}+1}{(x+1)^{2}}dx
integral of (-3x^2+2x+5)	\int\:(-3x^{2}+2x+5)dx
derivative of 2x^3+6xy^2-3x^2+3y^2	\frac{d}{dx}(2x^{3}+6xy^{2}-3x^{2}+3y^{2})
taylor cos(3x),2.5	taylor\:\cos(3x),2.5
laplacetransform 1-t	laplacetransform\:1-t
integral of (sqrt(x)+3)/(x+3)	\int\:\frac{\sqrt{x}+3}{x+3}dx
integral of sin(x)cos(x)e^x	\int\:\sin(x)\cos(x)e^{x}dx
derivative of (x^2/(x^2+4))	\frac{d}{dx}(\frac{x^{2}}{x^{2}+4})
integral of 1/((9x^2-1)^{3/2)}	\int\:\frac{1}{(9x^{2}-1)^{\frac{3}{2}}}dx
derivative of (1-4x/(6+x))	\frac{d}{dx}(\frac{1-4x}{6+x})
integral of 1/((u^2+9)^{5/2)}	\int\:\frac{1}{(u^{2}+9)^{\frac{5}{2}}}du
derivative of x^2log_{10}(x)	\frac{d}{dx}(x^{2}\log_{10}(x))
derivative of 7tan(x)	\frac{d}{dx}(7\tan(x))
integral from 1 to infinity of xe^{-x}	\int\:_{1}^{\infty\:}xe^{-x}dx
derivative of-1/5 (x^{-5}-x^{10})	\frac{d}{dx}(-\frac{1}{5}(x^{-5}-x^{10}))
(\partial)/(\partial v)(u*sin(v))	\frac{\partial\:}{\partial\:v}(u\cdot\:\sin(v))
limit as x approaches (0)+of (ln(x))/x	\lim\:_{x\to\:(0)+}(\frac{\ln(x)}{x})
derivative of f(x)=\|x-2\|	derivative\:f(x)=\left\|x-2\right\|
limit as x approaches-1 of (x+3)/(x+1)	\lim\:_{x\to\:-1}(\frac{x+3}{x+1})
d/(dz)(2^zlog_{2}(z))	\frac{d}{dz}(2^{z}\log_{2}(z))
derivative of (x^2-3/(x^3))	\frac{d}{dx}(\frac{x^{2}-3}{x^{3}})
3x^'+6x=4	3x^{\prime\:}+6x=4
(rdθ)/(dr)=θ^2+1	\frac{rdθ}{dr}=θ^{2}+1
tangent of f(x)=5-x^2,\at x=1	tangent\:f(x)=5-x^{2},\at\:x=1
derivative of x^2-7	derivative\:x^{2}-7
limit as x approaches 4+of 3/(x-4)	\lim\:_{x\to\:4+}(\frac{3}{x-4})
2y^'-y^2+4=0	2y^{\prime\:}-y^{2}+4=0
integral of (x^3)/(sqrt(1-2x^2))	\int\:\frac{x^{3}}{\sqrt{1-2x^{2}}}dx
derivative of 3xe^{3x}	derivative\:3xe^{3x}
d/(dy)(ye^{xy})	\frac{d}{dy}(ye^{xy})
6(dy)/(dt)-2y=ty^4,y(0)=-2	6\frac{dy}{dt}-2y=ty^{4},y(0)=-2
d/(dt)(7sin(t))	\frac{d}{dt}(7\sin(t))
derivative of t/((t-3)^2)	derivative\:\frac{t}{(t-3)^{2}}
derivative of sin^x(x)	\frac{d}{dx}(\sin^{x}(x))
integral of sinh(1-2x)	\int\:\sinh(1-2x)dx

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