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Popular Calculus Problems

(\partial)/(\partial x)(sin(x)ln(x^4+1/x))	\frac{\partial\:}{\partial\:x}(\sin(x)\ln(x^{4}+\frac{1}{x}))
e^y+ycos(x)+(xe^y+sin(x))(dy)/(dx)=0	e^{y}+y\cos(x)+(xe^{y}+\sin(x))\frac{dy}{dx}=0
integral of 4x^3-3x^2+6x-1	\int\:4x^{3}-3x^{2}+6x-1dx
taylor e^x-e^{-x}	taylor\:e^{x}-e^{-x}
derivative of e^{5xy}	\frac{d}{dx}(e^{5xy})
integral of 14(x-5)^6	\int\:14(x-5)^{6}dx
(\partial)/(\partial θ)(z)	\frac{\partial\:}{\partial\:θ}(z)
derivative of (2x-5^{-1}*(4x+3)^{-1})	\frac{d}{dx}((2x-5)^{-1}\cdot\:(4x+3)^{-1})
integral from 0 to 3 of (9e^{9x})/(1+e^{9x)}	\int\:_{0}^{3}\frac{9e^{9x}}{1+e^{9x}}dx
inverse oflaplace f(s0)=s-3(s2+4s+13)	inverselaplace\:f(s0)=s-3(s2+4s+13)
integral of 1/(x^5+16x^3+64x)	\int\:\frac{1}{x^{5}+16x^{3}+64x}dx
tangent of sqrt(3x+7),\at x=3	tangent\:\sqrt{3x+7},\at\:x=3
limit as x approaches 2 of 6x+1	\lim\:_{x\to\:2}(6x+1)
integral from-infinity to-1 of 1/(x^2)	\int\:_{-\infty\:}^{-1}\frac{1}{x^{2}}dx
integral of (x^2+1)/x*ln(x)	\int\:\frac{x^{2}+1}{x}\cdot\:\ln(x)dx
derivative of 3/(2x+4)+9x^2	derivative\:\frac{3}{2x+4}+9x^{2}
limit as x approaches 0+of (1-2x)^{3/x}	\lim\:_{x\to\:0+}((1-2x)^{\frac{3}{x}})
integral of (sqrt(x)(x+1))/(4x^4)	\int\:\frac{\sqrt{x}(x+1)}{4x^{4}}dx
(\partial)/(\partial x)(yln(x+y))	\frac{\partial\:}{\partial\:x}(y\ln(x+y))
integral of 16e^{-16x}	\int\:16e^{-16x}dx
derivative of (ln(x))^{ln(x)}	derivative\:(\ln(x))^{\ln(x)}
limit as x approaches 0 of (10sin(3x))/(1-cos(3x))	\lim\:_{x\to\:0}(\frac{10\sin(3x)}{1-\cos(3x)})
(\partial)/(\partial x)(e^{(x^2)/(y^3)})	\frac{\partial\:}{\partial\:x}(e^{\frac{x^{2}}{y^{3}}})
integral of 6x^5-4x^2+7/3	\int\:6x^{5}-4x^{2}+\frac{7}{3}dx
limit as t approaches 0 of f(t)	\lim\:_{t\to\:0}(f(t))
derivative of (2x-3/(x-1))	\frac{d}{dx}(\frac{2x-3}{x-1})
limit as x approaches 0 of e^{-2f(x)}	\lim\:_{x\to\:0}(e^{-2f(x)})
(\partial)/(\partial x)(1/(1-y))	\frac{\partial\:}{\partial\:x}(\frac{1}{1-y})
limit as t approaches 0 of (sin(-4t))/t	\lim\:_{t\to\:0}(\frac{\sin(-4t)}{t})
laplacetransform sqrt(h)	laplacetransform\:\sqrt{h}
limit as x approaches 1 of ((x+1)^2-1)/x	\lim\:_{x\to\:1}(\frac{(x+1)^{2}-1}{x})
limit as x approaches a of cf(x)	\lim\:_{x\to\:a}(cf(x))
derivative of f(x)=1-2sqrt(x)	derivative\:f(x)=1-2\sqrt{x}
derivative of ((7x-1(x+5))/(36x))	\frac{d}{dx}(\frac{(7x-1)(x+5)}{36x})
limit as x approaches 0 of 3-4/x	\lim\:_{x\to\:0}(3-\frac{4}{x})
integral of sin(3x)	\int\:\sin(3x)dx
derivative of 6/(1+6x)	\frac{d}{dx}(\frac{6}{1+6x})
integral of (5x^{14}-11x^{32})	\int\:(5x^{14}-11x^{32})dx
xdy=ydx	xdy=ydx
derivative of 3x^4ln(x)	\frac{d}{dx}(3x^{4}\ln(x))
integral of 8e^{2x}+6x	\int\:8e^{2x}+6xdx
(\partial)/(\partial x)(9xarctan(x/y))	\frac{\partial\:}{\partial\:x}(9x\arctan(\frac{x}{y}))
y=e^{-x}sin(pi)x	y=e^{-x}\sin(π)x
limit as x approaches 1 of {3f(x)-2h(x)}	\lim\:_{x\to\:1}(\left\{3f(x)-2h(x)\right\})
limit as x approaches 0 of (cos(3x))/(x+3)	\lim\:_{x\to\:0}(\frac{\cos(3x)}{x+3})
derivative of (x+1^{-2})	\frac{d}{dx}((x+1)^{-2})
y^{''}+4y^'+5y=5x+5e^{-x}	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=5x+5e^{-x}
integral of 2/(sqrt(36-25y^2))	\int\:\frac{2}{\sqrt{36-25y^{2}}}dy
sum from n=0 to infinity of na^n	\sum\:_{n=0}^{\infty\:}na^{n}
derivative of ln(x^2+2x+4)	\frac{d}{dx}(\ln(x^{2}+2x+4))
integral of e^{-st}(t-10)	\int\:e^{-st}(t-10)dt
laplacetransform sin(4t-5)	laplacetransform\:\sin(4t-5)
(\partial)/(\partial x)(xy(1-x^2-y^2))	\frac{\partial\:}{\partial\:x}(xy(1-x^{2}-y^{2}))
derivative of 2/(x-4)	\frac{d}{dx}(\frac{2}{x-4})
integral of x/(sqrt(4x+1))	\int\:\frac{x}{\sqrt{4x+1}}dx
(6xy-2y^2+1)dx+(3x^2-4xy)dy=0	(6xy-2y^{2}+1)dx+(3x^{2}-4xy)dy=0
integral of 5/(6x+5)	\int\:\frac{5}{6x+5}dx
derivative of x/(7x^2+1)	derivative\:\frac{x}{7x^{2}+1}
derivative of f(x)=e^{2e^x}	derivative\:f(x)=e^{2e^{x}}
derivative of e^x(acos(x+bsin(x)))	\frac{d}{dx}(e^{x}(a\cos(x)+b\sin(x)))
integral of x^6e^{-x^7}	\int\:x^{6}e^{-x^{7}}dx
tangent of y=x^2-4x+3,(1,0)	tangent\:y=x^{2}-4x+3,(1,0)
derivative of (x(1+{z}(x))/(1-{z)(x)})	\frac{d}{dx}(\frac{x(1+{z}(x))}{1-{z}(x)})
(dy)/(dx)=5xe^{6y}	\frac{dy}{dx}=5xe^{6y}
area 3x+18,x^2	area\:3x+18,x^{2}
limit as x approaches infinity of xe^x	\lim\:_{x\to\:\infty\:}(xe^{x})
limit as x approaches 0+of (x^2-1)/(x-1)	\lim\:_{x\to\:0+}(\frac{x^{2}-1}{x-1})
integral of 1/(5-4x^2)	\int\:\frac{1}{5-4x^{2}}dx
derivative of sin(x)+cos(x)	derivative\:\sin(x)+\cos(x)
integral of (4-x^2)^{3/2}x	\int\:(4-x^{2})^{\frac{3}{2}}xdx
derivative of (xx^2cos(x))	\frac{d}{dx}((x)x^{2}\cos(x))
limit as x approaches 0 of (1+2x)^{6/x}	\lim\:_{x\to\:0}((1+2x)^{\frac{6}{x}})
sum from n=2 to infinity of ln(ln(n))	\sum\:_{n=2}^{\infty\:}\ln(\ln(n))
limit as x approaches 3 of sqrt(3x-5)	\lim\:_{x\to\:3}(\sqrt{3x-5})
integral of+tln(t+5)	\int\:+t\ln(t+5)dt
derivative of 3/(2+tan(x))	\frac{d}{dx}(\frac{3}{2+\tan(x)})
integral of (tan(x))/(sin(x)cos(x))	\int\:\frac{\tan(x)}{\sin(x)\cos(x)}dx
(dy)/(dx)=(2sec(y))/((x+1)^2)	\frac{dy}{dx}=\frac{2\sec(y)}{(x+1)^{2}}
integral of ((cos(x)))/(3-sin(x))	\int\:\frac{(\cos(x))}{3-\sin(x)}dx
f(x)=(e^x+e^{-x})/2	f(x)=\frac{e^{x}+e^{-x}}{2}
y^{''}+11y^'+24y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+11y^{\prime\:}+24y=0,y(0)=1,y^{\prime\:}(0)=0
limit as t approaches 0 of 2/t-2/(e^t-1)	\lim\:_{t\to\:0}(\frac{2}{t}-\frac{2}{e^{t}-1})
derivative of (x^8-1^3)	\frac{d}{dx}((x^{8}-1)^{3})
integral of cot^2(xcs)c^4x	\int\:\cot^{2}(xcs)c^{4}xdx
derivative of-2(x+3(x-3)^2)	\frac{d}{dx}(-2(x+3)(x-3)^{2})
derivative of (cos(y+2e^{-x}cos(x))/y)	\frac{d}{dx}(\frac{\cos(y)+2e^{-x}\cos(x)}{y})
tangent of y=3xe^x,(0,0)	tangent\:y=3xe^{x},(0,0)
y^'=xy+x	y^{\prime\:}=xy+x
(dy)/(dt)+6y=0	\frac{dy}{dt}+6y=0
integral from-1 to 1 of (2-2x^2)^2	\int\:_{-1}^{1}(2-2x^{2})^{2}dx
integral of tan^7(x)sec^5(x)	\int\:\tan^{7}(x)\sec^{5}(x)dx
y^{''}-3y^'+2y=4	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=4
derivative of (4ln(x)/x)	\frac{d}{dx}(\frac{4\ln(x)}{x})
(\partial)/(\partial x)(y-1/x)	\frac{\partial\:}{\partial\:x}(y-\frac{1}{x})
y^'-y=4x	y^{\prime\:}-y=4x
(\partial)/(\partial x)(arctan(xsqrt(t)))	\frac{\partial\:}{\partial\:x}(\arctan(x\sqrt{t}))
derivative of y=x^2+2	derivative\:y=x^{2}+2
(\partial)/(\partial x)(4ye^{4xy})	\frac{\partial\:}{\partial\:x}(4ye^{4xy})
derivative of 4x-8	\frac{d}{dx}(4x-8)
derivative of f(θ)=(sec(θ))/(1+sec(θ))	derivative\:f(θ)=\frac{\sec(θ)}{1+\sec(θ)}

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