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Popular Calculus Problems

derivative of f(x)= 1/2 b(1/x-1/(x^0))^2	derivative\:f(x)=\frac{1}{2}b(\frac{1}{x}-\frac{1}{x^{0}})^{2}
tangent of f(x)=x^3-5x^2+7,\at x=1	tangent\:f(x)=x^{3}-5x^{2}+7,\at\:x=1
integral of (x+5)/(x^2+2x-15)	\int\:\frac{x+5}{x^{2}+2x-15}dx
integral of 1/(x(ln(x^2))^3)	\int\:\frac{1}{x(\ln(x^{2}))^{3}}dx
limit as x approaches 5+of sqrt(x^2-25)	\lim\:_{x\to\:5+}(\sqrt{x^{2}-25})
integral of 0.6x^2	\int\:0.6x^{2}dx
limit as x approaches+0 of ln(x)	\lim\:_{x\to\:+0}(\ln(x))
derivative of (3x)/(1-x)	derivative\:\frac{3x}{1-x}
integral of sec(x)-1	\int\:\sec(x)-1dx
inverse oflaplace (15)/(s(3s+5))	inverselaplace\:\frac{15}{s(3s+5)}
integral of (2x)/1 ^2	\int\:\frac{d^{2}x}{1}dt^{2}
inverse oflaplace 1/(s^2+s/4)	inverselaplace\:\frac{1}{s^{2}+\frac{s}{4}}
derivative of f(x)=(xtan^2(x))/(1+x^2)	derivative\:f(x)=\frac{x\tan^{2}(x)}{1+x^{2}}
integral of 3x^2+6	\int\:3x^{2}+6dx
derivative of \sqrt[3]{5+9x^2}	derivative\:\sqrt[3]{5+9x^{2}}
limit as x approaches 5 of ln(x-5)	\lim\:_{x\to\:5}(\ln(x-5))
derivative of e+L(x)	\frac{d}{dx}(e+L(x))
derivative of (x^3)/4	derivative\:\frac{x^{3}}{4}
slope of y^3-xy^2=4	slope\:y^{3}-xy^{2}=4
derivative of y= 3/(sqrt(x+7))	derivative\:y=\frac{3}{\sqrt{x+7}}
integral of 1/(sqrt(16-49x^2))	\int\:\frac{1}{\sqrt{16-49x^{2}}}dx
derivative of (x^2+2x+3/(x^2))	\frac{d}{dx}(\frac{x^{2}+2x+3}{x^{2}})
integral of 1/((y+2)^2)	\int\:\frac{1}{(y+2)^{2}}dy
(dy)/(dx)+3x^2y=x	\frac{dy}{dx}+3x^{2}y=x
limit as x approaches 1 of x^4-x^2+2	\lim\:_{x\to\:1}(x^{4}-x^{2}+2)
y^'+0.4y=0.7(299e^{-0.7x})	y^{\prime\:}+0.4\cdot\:y=0.7\cdot\:(299\cdot\:e^{-0.7\cdot\:x})
limit as x approaches 1+of 2^{1/(x-1)}	\lim\:_{x\to\:1+}(2^{\frac{1}{x-1}})
x(2y-3)dx+(x^2+1)dy=0	x(2y-3)dx+(x^{2}+1)dy=0
limit as x approaches 1 of 7x+a	\lim\:_{x\to\:1}(7x+a)
y^'=(2y)/x ,y(2)=4	y^{\prime\:}=\frac{2y}{x},y(2)=4
(2y^2+6x)dx+2xydy=0	(2y^{2}+6x)dx+2xydy=0
derivative of ln((x+6/(x-6)))	\frac{d}{dx}(\ln(\frac{x+6}{x-6}))
integral of (tan^2(7x))/(csc(7x))	\int\:\frac{\tan^{2}(7x)}{\csc(7x)}dx
derivative of f(x)=sqrt(x)(x-6)^2	derivative\:f(x)=\sqrt{x}(x-6)^{2}
derivative of 5e^x+4/(\sqrt[3]{x)}	derivative\:5e^{x}+\frac{4}{\sqrt[3]{x}}
derivative of 2sin(x+1)	\frac{d}{dx}(2\sin(x)+1)
(\partial)/(\partial x)(-1/(2x)+1/(2x^2))	\frac{\partial\:}{\partial\:x}(-\frac{1}{2x}+\frac{1}{2x^{2}})
derivative of x^4sin(3x)	\frac{d}{dx}(x^{4}\sin(3x))
integral of 6/(x+1)	\int\:\frac{6}{x+1}dx
derivative of y=xsin(3/x)	derivative\:y=x\sin(\frac{3}{x})
integral of (x^7)/(sqrt(x^4-3))	\int\:\frac{x^{7}}{\sqrt{x^{4}-3}}dx
slope of (-7,-4),(8,8)	slope\:(-7,-4),(8,8)
sum from n=1 to infinity of (6^n)/((4+11^n))	\sum\:_{n=1}^{\infty\:}\frac{6^{n}}{(4+11^{n})}
integral of 4/(x^2+25)	\int\:\frac{4}{x^{2}+25}dx
derivative of (6x)/(e^x)	derivative\:\frac{6x}{e^{x}}
xy^'+6y=-35xcos(x^7)	xy^{\prime\:}+6y=-35x\cos(x^{7})
integral of x^3sqrt(12+x^4)	\int\:x^{3}\sqrt{12+x^{4}}dx
sum from n=1 to infinity of (-1)^n	\sum\:_{n=1}^{\infty\:}(-1)^{n}
derivative of 9x-5	\frac{d}{dx}(9x-5)
integral of (x-8)^{3/2}	\int\:(x-8)^{\frac{3}{2}}dx
derivative of e^{2xy}	\frac{d}{dx}(e^{2xy})
derivative of f(x)=x^2(1-4x)	derivative\:f(x)=x^{2}(1-4x)
tangent of f(x)=x^3-6x^2-34x+40,\at x=-3	tangent\:f(x)=x^{3}-6x^{2}-34x+40,\at\:x=-3
integral from 0 to 7 of xsqrt(49-x^2)	\int\:_{0}^{7}x\sqrt{49-x^{2}}dx
integral from 0 to 2 of x(x^2-1)^3	\int\:_{0}^{2}x(x^{2}-1)^{3}dx
(\partial)/(\partial x)(x^2y+4x^4y)	\frac{\partial\:}{\partial\:x}(x^{2}y+4x^{4}y)
sum from n=3 to infinity of 1/(n(n+1))	\sum\:_{n=3}^{\infty\:}\frac{1}{n(n+1)}
integral of (ae^θ+b)/(ae^θ-b)	\int\:\frac{ae^{θ}+b}{ae^{θ}-b}dθ
y= 1/(1+e^{-x)}	y=\frac{1}{1+e^{-x}}
(\partial)/(\partial x)(e^{2x}sin(2y))	\frac{\partial\:}{\partial\:x}(e^{2x}\sin(2y))
limit as x approaches 2 of (x^2-4)/(x+2)	\lim\:_{x\to\:2}(\frac{x^{2}-4}{x+2})
2x^{''}-3x^'+x=0	2x^{\prime\:\prime\:}-3x^{\prime\:}+x=0
derivative of ((1/x+1/(x^2))/(x-1))	\frac{d}{dx}(\frac{(\frac{1}{x}+\frac{1}{x^{2}})}{x-1})
(dy)/(dx)=1-e^{y-x+5}	\frac{dy}{dx}=1-e^{y-x+5}
integral from 0 to 1 of 6cos(3x)	\int\:_{0}^{1}6\cos(3x)dx
limit as x approaches 1-of 2/(ln(x))	\lim\:_{x\to\:1-}(\frac{2}{\ln(x)})
slope ofintercept (0,9),(7,4)	slopeintercept\:(0,9),(7,4)
derivative of 7x^2tan(x)	\frac{d}{dx}(7x^{2}\tan(x))
laplacetransform 6t^3e^{-2t}	laplacetransform\:6t^{3}e^{-2t}
integral of 1/((1+4x^2)(arctan(2x))^3)	\int\:\frac{1}{(1+4x^{2})(\arctan(2x))^{3}}dx
integral of sin^4(6x)	\int\:\sin^{4}(6x)dx
limit as x approaches 0+of 3x^{sqrt(x)}	\lim\:_{x\to\:0+}(3x^{\sqrt{x}})
2x^2y^{''}+6xy^'+2y=0,y(1)=2,y^'(1)=-1	2x^{2}y^{\prime\:\prime\:}+6xy^{\prime\:}+2y=0,y(1)=2,y^{\prime\:}(1)=-1
y^{''}-6y^'+9y=2te^{3t}	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=2te^{3t}
limit as x approaches 2-of 4/((x-2)^5)	\lim\:_{x\to\:2-}(\frac{4}{(x-2)^{5}})
y^'-y=4sin(3t)	y^{\prime\:}-y=4\sin(3t)
inverse oflaplace 1/(s-1)	inverselaplace\:\frac{1}{s-1}
sum from n=4 to infinity of 1/((n)(n+1))	\sum\:_{n=4}^{\infty\:}\frac{1}{(n)(n+1)}
integral from 0 to x of 1/((1-x))	\int\:_{0}^{x}\frac{1}{(1-x)}dx
limit as x approaches 0 of 1/(1-e^x)	\lim\:_{x\to\:0}(\frac{1}{1-e^{x}})
sum from n=1 to infinity of (cos(32))^n	\sum\:_{n=1}^{\infty\:}(\cos(32))^{n}
(\partial)/(\partial x)(x^3-9xy+7y^3)	\frac{\partial\:}{\partial\:x}(x^{3}-9xy+7y^{3})
derivative of 750+12x-0.8x^7	\frac{d}{dx}(750+12x-0.8x^{7})
maclaurin cos(x^4)	maclaurin\:\cos(x^{4})
derivative of (ln(2x)dx)	\frac{d}{dx}((\ln(2x))dx)
derivative of x*e^{-x}	derivative\:x\cdot\:e^{-x}
integral of 35x^4	\int\:35x^{4}dx
derivative of (3+x/(1-3x))	\frac{d}{dx}(\frac{3+x}{1-3x})
area y=(4x)/(1+x^2),y=(4x^2)/(1+x^3)	area\:y=\frac{4x}{1+x^{2}},y=\frac{4x^{2}}{1+x^{3}}
(\partial)/(\partial x)(4ax^4+7b(x,t)t^3)	\frac{\partial\:}{\partial\:x}(4ax^{4}+7b(x,t)t^{3})
derivative of y=(4+xf(x))/(sqrt(x))	derivative\:y=\frac{4+xf(x)}{\sqrt{x}}
integral of xe^{-2}+ex^{-2}	\int\:xe^{-2}+ex^{-2}dx
(\partial)/(\partial z)(xy^2z^3)	\frac{\partial\:}{\partial\:z}(xy^{2}z^{3})
derivative of arctan((x-1)/(x+1))	derivative\:\arctan(\frac{x-1}{x+1})
integral of (e^{3x})/(1-2e^{3x)}	\int\:\frac{e^{3x}}{1-2e^{3x}}dx
derivative of ln(sin(x))	derivative\:\ln(\sin(x))
y^'=yx^2	y^{\prime\:}=yx^{2}
laplacetransform t^3cos(3t)	laplacetransform\:t^{3}\cos(3t)
derivative of sqrt(1+(x^2))	\frac{d}{dx}(\sqrt{1+(x)^{2}})
integral of x9^x	\int\:x9^{x}dx

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