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Popular Calculus Problems

tangent of f(x)=4x^2+7x	tangent\:f(x)=4x^{2}+7x
integral of 1/(u^2-4)	\int\:\frac{1}{u^{2}-4}du
d/(dθ)(sqrt(θ))	\frac{d}{dθ}(\sqrt{θ})
integral of sin(7x)cos(7x)	\int\:\sin(7x)\cos(7x)dx
(\partial)/(\partial x)((x-y)/(2xy+5))	\frac{\partial\:}{\partial\:x}(\frac{x-y}{2xy+5})
derivative of (sin(x))^x	derivative\:(\sin(x))^{x}
integral of 30x^5	\int\:30x^{5}dx
tangent of x^3-2x+2(4.58)	tangent\:x^{3}-2x+2(4.58)
(\partial)/(\partial x)(3x-7y)	\frac{\partial\:}{\partial\:x}(3x-7y)
y^'cos(x)+ysin(x)=2cos^3(x)sin(x)	y^{\prime\:}\cos(x)+y\sin(x)=2\cos^{3}(x)\sin(x)
limit as h approaches 0 of (2^{-h}-1)/h	\lim\:_{h\to\:0}(\frac{2^{-h}-1}{h})
derivative of arcsin(x/3)+C	derivative\:\arcsin(\frac{x}{3})+C
integral of (54)/((9x+5)^7)	\int\:\frac{54}{(9x+5)^{7}}dx
integral of 6sin^2(3x)	\int\:6\sin^{2}(3x)dx
derivative of f(x)=(1-5x)/(1+7x)	derivative\:f(x)=\frac{1-5x}{1+7x}
derivative of cot(3x)	\frac{d}{dx}(\cot(3x))
integral of sin^7(x)cos(x)	\int\:\sin^{7}(x)\cos(x)dx
sum from n=0 to infinity of n^2e^{-n}	\sum\:_{n=0}^{\infty\:}n^{2}e^{-n}
derivative of-3/(3x+2)	\frac{d}{dx}(-\frac{3}{3x+2})
integral from-14 to 1 of x\|49-x^2\|	\int\:_{-14}^{1}x\left\|49-x^{2}\right\|dx
derivative of e^tsin(9t)	derivative\:e^{t}\sin(9t)
derivative of sin((pix/2))	\frac{d}{dx}(\sin(\frac{πx}{2}))
integral of (3x^2+6x+2)/(x(x+1)^2)	\int\:\frac{3x^{2}+6x+2}{x(x+1)^{2}}dx
derivative of x^3+x^{1/2}+2	\frac{d}{dx}(x^{3}+x^{\frac{1}{2}}+2)
(\partial)/(\partial y)((2x)/(x^2+y^4))	\frac{\partial\:}{\partial\:y}(\frac{2x}{x^{2}+y^{4}})
tangent of f(x-pi)	tangent\:f(x-π)
f(x)=tan(x)-1	f(x)=\tan(x)-1
(\partial)/(\partial x)(5e^xcos(yz))	\frac{\partial\:}{\partial\:x}(5e^{x}\cos(yz))
integral from 0 to 1 of (e^{-2x})	\int\:_{0}^{1}(e^{-2x})dx
derivative of 5/(8x^8)	\frac{d}{dx}(\frac{5}{8x^{8}})
derivative of (x^2)/(4(2-x))	derivative\:\frac{x^{2}}{4(2-x)}
integral of 9y^{-2}	\int\:9y^{-2}dy
derivative of f(x)=\|x^2-25\|	derivative\:f(x)=\left\|x^{2}-25\right\|
limit as x approaches 0 of (sin(6x))/(sin(9x))	\lim\:_{x\to\:0}(\frac{\sin(6x)}{\sin(9x)})
ty^'+(t+1)y=t,y(ln(7))=1	ty^{\prime\:}+(t+1)y=t,y(\ln(7))=1
derivative of 5x^3+2ln(x)	\frac{d}{dx}(5x^{3}+2\ln(x))
limit as x approaches 1 of (x-5)/(x-1)	\lim\:_{x\to\:1}(\frac{x-5}{x-1})
derivative of e^{(x^2+x})	\frac{d}{dx}(e^{(x^{2}+x)})
limit as x approaches 3 of 4x^2+1	\lim\:_{x\to\:3}(4x^{2}+1)
derivative of x^2+9	derivative\:x^{2}+9
sum from n=1 to infinity of 1/(9n+3n-2)	\sum\:_{n=1}^{\infty\:}\frac{1}{9n+3n-2}
derivative of (x+7)/(x-7)	derivative\:\frac{x+7}{x-7}
derivative of ((2x+1))/(sqrt(x^3))	derivative\:\frac{(2x+1)}{\sqrt{x^{3}}}
integral from 1 to 2 of x^2+1/(4x^2)	\int\:_{1}^{2}x^{2}+\frac{1}{4x^{2}}dx
f(x)=1-e^{-x}	f(x)=1-e^{-x}
derivative of-5ln(sin(x))	derivative\:-5\ln(\sin(x))
integral of sqrt(4/(9-9x^2))	\int\:\sqrt{\frac{4}{9-9x^{2}}}dx
tangent of x^2+9(-5.34)	tangent\:x^{2}+9(-5.34)
limit as x approaches 0 of 3x^2-2x+4	\lim\:_{x\to\:0}(3x^{2}-2x+4)
derivative of 15x^5-(60/(7x^6)-1)	\frac{d}{dx}(15x^{5}-\frac{60}{7x^{6}}-1)
integral of r/((r^2+z^2)^{3/2)}	\int\:\frac{r}{(r^{2}+z^{2})^{\frac{3}{2}}}dr
derivative of (-4x/(x^4-2x^2+1))	\frac{d}{dx}(\frac{-4x}{x^{4}-2x^{2}+1})
limit as x approaches a of f(x)(x)^{g(x)}	\lim\:_{x\to\:a}(f(x)(x)^{g(x)})
derivative of (x^2/(16))	\frac{d}{dx}(\frac{x^{2}}{16})
integral of sec^2(x)+tan(x)	\int\:\sec^{2}(x)+\tan(x)dx
derivative of f(x(3x^2+5))	\frac{d}{dx}(f(x)(3x^{2}+5))
(\partial)/(\partial x)(y^2-x)	\frac{\partial\:}{\partial\:x}(y^{2}-x)
inverse oflaplace ((85))/((18s+90))	inverselaplace\:\frac{(85)}{(18s+90)}
derivative of (70x/((3x^2+8)^2))	\frac{d}{dx}(\frac{70x}{(3x^{2}+8)^{2}})
limit as x approaches infinity of (x^2)/(e^{4x)}	\lim\:_{x\to\:\infty\:}(\frac{x^{2}}{e^{4x}})
derivative of 3arctan(x+sqrt(1+x^2))	derivative\:3\arctan(x+\sqrt{1+x^{2}})
integral of (cot(x))/(sin^2(x))	\int\:\frac{\cot(x)}{\sin^{2}(x)}dx
sum from n=0 to infinity of x(1-x)^{n-1}	\sum\:_{n=0}^{\infty\:}x(1-x)^{n-1}
integral of sqrt(1-4x^2)	\int\:\sqrt{1-4x^{2}}dx
derivative of (x^2+1(x+1)^2)	\frac{d}{dx}((x^{2}+1)(x+1)^{2})
(\partial)/(\partial x)(9e^xln(y))	\frac{\partial\:}{\partial\:x}(9e^{x}\ln(y))
(dy)/(dx)=(e^x+5)^2	\frac{dy}{dx}=(e^{x}+5)^{2}
integral of 1/((1+sqrt(x))^5\sqrt{x)}	\int\:\frac{1}{(1+\sqrt{x})^{5}\sqrt{x}}dx
limit as x approaches 0 of (sin^2(2x))/x	\lim\:_{x\to\:0}(\frac{\sin^{2}(2x)}{x})
derivative of f(x)=tan(e^x)	derivative\:f(x)=\tan(e^{x})
derivative of (x^2-5x)/(x+1)	derivative\:\frac{x^{2}-5x}{x+1}
sum from n=0 to infinity of (5^n)/(n!)	\sum\:_{n=0}^{\infty\:}\frac{5^{n}}{n!}
integral of 8e^{-2x}	\int\:8e^{-2x}dx
taylor x^2cos(x),pi	taylor\:x^{2}\cos(x),π
integral of 1/(2^x)	\int\:\frac{1}{2^{x}}dx
derivative of y=x^2sin^9(x)+xcos^{-4}(x)	derivative\:y=x^{2}\sin^{9}(x)+x\cos^{-4}(x)
integral of 1/(x^2sqrt(4x^2+9))	\int\:\frac{1}{x^{2}\sqrt{4x^{2}+9}}dx
derivative of f(x)=6x^3-27/2 x^2+3	derivative\:f(x)=6x^{3}-\frac{27}{2}x^{2}+3
derivative of (8x+5^2)	\frac{d}{dx}((8x+5)^{2})
derivative of 8/(7x^2)	derivative\:\frac{8}{7x^{2}}
derivative of (5x^6+8x^3)^4	derivative\:(5x^{6}+8x^{3})^{4}
inverse oflaplace 2/(s(0.12s+1))	inverselaplace\:\frac{2}{s(0.12s+1)}
xy^'=y+7x^2sin(x)	xy^{\prime\:}=y+7x^{2}\sin(x)
(\partial)/(\partial x)(xy^{1/2})	\frac{\partial\:}{\partial\:x}(xy^{\frac{1}{2}})
derivative of R(t)=50t^2e^{-t}+8	derivative\:R(t)=50t^{2}e^{-t}+8
derivative of 4x^3-2x^2	\frac{d}{dx}(4x^{3}-2x^{2})
y^{''}-8y^'+16y=t^{-3}e^{4t}	y^{\prime\:\prime\:}-8y^{\prime\:}+16y=t^{-3}e^{4t}
(16+x^2)((dy)/(dx))-2xy=0	(16+x^{2})(\frac{dy}{dx})-2xy=0
derivative of ln((x^2)/(3-x))	derivative\:\ln(\frac{x^{2}}{3-x})
(dy)/(dx)=3y^{2/3}	\frac{dy}{dx}=3y^{\frac{2}{3}}
(\partial)/(\partial y)(2xy^4+2)	\frac{\partial\:}{\partial\:y}(2xy^{4}+2)
limit as x approaches 0 of 1/(2x)	\lim\:_{x\to\:0}(\frac{1}{2x})
derivative of (x^3-x+3x^{3/2}/(sqrt(x)))	\frac{d}{dx}(\frac{x^{3}-x+3x^{\frac{3}{2}}}{\sqrt{x}})
derivative of x/(1-ln(x))	\frac{d}{dx}(\frac{x}{1-\ln(x)})
y^'=0.002y-200	y^{\prime\:}=0.002y-200
integral from 1/2 to 1 of (4y+5)/(y^2+y)	\int\:_{\frac{1}{2}}^{1}\frac{4y+5}{y^{2}+y}dy
integral from-5 to 5 of 1/(x^{(2/3))}	\int\:_{-5}^{5}\frac{1}{x^{(\frac{2}{3})}}dx
slope of (0,-3),(2,1)	slope\:(0,-3),(2,1)
derivative of 1/3	derivative\:\frac{1}{3}
integral of (x^2+1)^2(2x)	\int\:(x^{2}+1)^{2}(2x)dx

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