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Popular Calculus Problems

derivative of h(t)=6ln(t^8)	derivative\:h(t)=6\ln(t^{8})
derivative of sqrt(144-x)	\frac{d}{dx}(\sqrt{144-x})
integral of (5-x^3)^4x^2	\int\:(5-x^{3})^{4}x^{2}dx
derivative of x^2sqrt(2x+3)	\frac{d}{dx}(x^{2}\sqrt{2x+3})
area x^2+4,-x^2-1,[-2,3]	area\:x^{2}+4,-x^{2}-1,[-2,3]
derivative of arcsec(x^{10})	\frac{d}{dx}(\arcsec(x^{10}))
derivative of (cos(pix-16)^4)	\frac{d}{dx}((\cos(πx-16))^{4})
integral of 1/(sqrt(-x^2-6x))	\int\:\frac{1}{\sqrt{-x^{2}-6x}}dx
area x=-y,x=2y+3,y=-2,y=1	area\:x=-y,x=2y+3,y=-2,y=1
derivative of xln(3)	\frac{d}{dx}(x\ln(3))
derivative of f(x)=sqrt(x)+1	derivative\:f(x)=\sqrt{x}+1
(dx)/(x(y-1))+(dy)/(y(x+2))=0,y(1)=1	\frac{dx}{x(y-1)}+\frac{dy}{y(x+2)}=0,y(1)=1
11x-4ysqrt(x^2+1)y^'=0,y(0)=7	11x-4y\sqrt{x^{2}+1}y^{\prime\:}=0,y(0)=7
limit as x approaches 5 of 4/(x-5)	\lim\:_{x\to\:5}(\frac{4}{x-5})
inverse oflaplace (s^3+5s^2+9s+7)/((s+1)*(s+2))	inverselaplace\:\frac{s^{3}+5s^{2}+9s+7}{(s+1)\cdot\:(s+2)}
derivative of ((x^2-6)^3)/(x^2+2)	derivative\:\frac{(x^{2}-6)^{3}}{x^{2}+2}
derivative of f(x)=3+1/(x^2)	derivative\:f(x)=3+\frac{1}{x^{2}}
integral of cos(2x)-sin(x)	\int\:\cos(2x)-\sin(x)dx
inverse oflaplace (2s)/((s^2+25))	inverselaplace\:\frac{2s}{(s^{2}+25)}
derivative of 0.1e^{0.5061(t)}	derivative\:0.1e^{0.5061(t)}
integral of ((ln^2(x)))/x	\int\:\frac{(\ln^{2}(x))}{x}dx
derivative of e^{-2x}cos(3x+sin(3x))	\frac{d}{dx}(e^{-2x}\cos(3x)+\sin(3x))
integral of xe^{2x}sin(3x)	\int\:xe^{2x}\sin(3x)dx
inverse oflaplace 2/(s^2+2s+1)	inverselaplace\:\frac{2}{s^{2}+2s+1}
taylor ((z^n))/(n!)	taylor\:\frac{(z^{n})}{n!}
integral of (2x)/(3x^2-1)	\int\:\frac{2x}{3x^{2}-1}dx
derivative of (4+x)/(1-4x)	derivative\:\frac{4+x}{1-4x}
integral of (x^2-4x-6)/(x^2-6x)	\int\:\frac{x^{2}-4x-6}{x^{2}-6x}dx
integral from 3 to 7 of x/(sqrt(7+x^2))	\int\:_{3}^{7}\frac{x}{\sqrt{7+x^{2}}}dx
derivative of (xln(x)/(e^x))	\frac{d}{dx}(\frac{x\ln(x)}{e^{x}})
(\partial)/(\partial x)(x^{1/3}y^{1/3})	\frac{\partial\:}{\partial\:x}(x^{\frac{1}{3}}y^{\frac{1}{3}})
derivative of 1/3 tan^3(x/2-tan(x/2))	\frac{d}{dx}(\frac{1}{3}\tan^{3}(\frac{x}{2})-\tan(\frac{x}{2}))
derivative of sec^4(2x^2)	\frac{d}{dx}(\sec^{4}(2)x^{2})
derivative of nx^n	\frac{d}{dx}(nx^{n})
derivative of (2x^2+8x+4)/(sqrt(x))	derivative\:\frac{2x^{2}+8x+4}{\sqrt{x}}
derivative of (-cos(x-1)/(x^3+x^2))	\frac{d}{dx}(\frac{-\cos(x)-1}{x^{3}+x^{2}})
tangent of y=1+4x^2-2x^3	tangent\:y=1+4x^{2}-2x^{3}
(\partial)/(\partial y)(x^3-xy^2+3y^2)	\frac{\partial\:}{\partial\:y}(x^{3}-xy^{2}+3y^{2})
tangent of y=4x^3-2x,(1,2)	tangent\:y=4x^{3}-2x,(1,2)
tangent of f(x)=x^2+1,(-4,17)	tangent\:f(x)=x^{2}+1,(-4,17)
2xy+x^2(dy)/(dx)=y^2	2xy+x^{2}\frac{dy}{dx}=y^{2}
derivative of (z^{8/3})/8-(e^{-2z})/2	derivative\:\frac{z^{\frac{8}{3}}}{8}-\frac{e^{-2z}}{2}
derivative of (3x+4/(2x-5))	\frac{d}{dx}(\frac{3x+4}{2x-5})
y^{''}-3y^'=0	y^{\prime\:\prime\:}-3y^{\prime\:}=0
limit as x approaches infinity of 7x+4	\lim\:_{x\to\:\infty\:}(7x+4)
tangent of f(x)=2x^2+5x	tangent\:f(x)=2x^{2}+5x
integral of (3x^5-5x^9)	\int\:(3x^{5}-5x^{9})dx
limit as x approaches y of (x^n-y^n)/(x-y)	\lim\:_{x\to\:y}(\frac{x^{n}-y^{n}}{x-y})
area e^{5x},e^{7x},1	area\:e^{5x},e^{7x},1
integral of 3x*e^{-2x}	\int\:3x\cdot\:e^{-2x}dx
integral of (x^2)/(sqrt(x^2+16))	\int\:\frac{x^{2}}{\sqrt{x^{2}+16}}dx
e^x(dy)/(dx)=e^{-y}+e^{-2x-y}	e^{x}\frac{dy}{dx}=e^{-y}+e^{-2x-y}
derivative of f(x)=cos(pix)	derivative\:f(x)=\cos(πx)
(\partial)/(\partial x)((7x+y)(e^x))	\frac{\partial\:}{\partial\:x}((7x+y)(e^{x}))
derivative of 2cos(x-3sin(x))	\frac{d}{dx}(2\cos(x)-3\sin(x))
integral of 9e^{-x}	\int\:9e^{-x}dx
derivative of (ln(x-5-2)^2)	\frac{d}{dx}((\ln(x-5)-2)^{2})
(dy)/(dx)=(3cos(x))/(e^{2y)}	\frac{dy}{dx}=\frac{3\cos(x)}{e^{2y}}
integral of (inx)/x	\int\:\frac{inx}{x}dx
derivative of y=-2	derivative\:y=-2
(\partial)/(\partial x)(pix)	\frac{\partial\:}{\partial\:x}(πx)
f^{''}(x)=6x+12x^2	f^{\prime\:\prime\:}(x)=6x+12x^{2}
integral of (ln(19x))/x	\int\:\frac{\ln(19x)}{x}dx
(\partial)/(\partial x)(5x^2y-1)	\frac{\partial\:}{\partial\:x}(5x^{2}y-1)
tangent of f(x)=(-4x)/(x^2+1),(1,2)	tangent\:f(x)=\frac{-4x}{x^{2}+1},(1,2)
integral of 3/(2x-1)	\int\:\frac{3}{2x-1}dx
y^{''}+4y=8t^2-20t+8	y^{\prime\:\prime\:}+4y=8t^{2}-20t+8
derivative of 4x^3+1/(x^2-x+3)	\frac{d}{dx}(4x^{3}+\frac{1}{x^{2}}-x+3)
derivative of (5x/((x^3-6)^2))	\frac{d}{dx}(\frac{5x}{(x^{3}-6)^{2}})
(\partial)/(\partial x)(3/(2x^2))	\frac{\partial\:}{\partial\:x}(\frac{3}{2x^{2}})
y^2y^'=x^2	y^{2}y^{\prime\:}=x^{2}
integral from 0 to pi/3 of xsin(12x)	\int\:_{0}^{\frac{π}{3}}x\sin(12x)dx
integral of x^{2/3}	\int\:x^{\frac{2}{3}}dx
derivative of f(x)=(sin^2(x))/(x^2)	derivative\:f(x)=\frac{\sin^{2}(x)}{x^{2}}
(dy)/(dx)=(y-1)^{-3}	\frac{dy}{dx}=(y-1)^{-3}
integral of (sin(θ))/(cos^2(θ)-cos(θ)-2)	\int\:\frac{\sin(θ)}{\cos^{2}(θ)-\cos(θ)-2}dθ
derivative of y(θ)=cos(θ^2)	derivative\:y(θ)=\cos(θ^{2})
limit as x approaches infinity of 2x^4	\lim\:_{x\to\:\infty\:}(2x^{4})
(dy)/(dx)=2y-xy	\frac{dy}{dx}=2y-xy
derivative of (-4x^2+1)^2	derivative\:(-4x^{2}+1)^{2}
limit as x approaches 1+of 3/x-2/(ln(x))	\lim\:_{x\to\:1+}(\frac{3}{x}-\frac{2}{\ln(x)})
y^'+ky=e^{-kx}	y^{\prime\:}+ky=e^{-kx}
derivative of sqrt(x)(1-5sqrt(x))	derivative\:\sqrt{x}(1-5\sqrt{x})
limit as x approaches 0 of 1-cos(2x)	\lim\:_{x\to\:0}(1-\cos(2x))
integral of 8/9 x^{-1/9}	\int\:\frac{8}{9}x^{-\frac{1}{9}}dx
limit as x approaches 3 of 3x	\lim\:_{x\to\:3}(3x)
integral of 1/9 x^2	\int\:\frac{1}{9}x^{2}dx
derivative of (((4x^3+2x^2)/(sin(x)))^2)	\frac{d}{dx}((\frac{(4x^{3}+2x^{2})}{\sin(x)})^{2})
area y=(-2x^2+3x-15)/(x^3-9x),x=1,x=2	area\:y=\frac{-2x^{2}+3x-15}{x^{3}-9x},x=1,x=2
integral of sin((2x)/3)	\int\:\sin(\frac{2x}{3})dx
derivative of ln((2x^{3x}))	\frac{d}{dx}(\ln((2x)^{3x}))
normal of y=x^2-3x,(3,0)	normal\:y=x^{2}-3x,(3,0)
t(t-4)y^'+y=0	t(t-4)y^{\prime\:}+y=0
limit as x approaches 2 of 9x^2	\lim\:_{x\to\:2}(9x^{2})
inverse oflaplace s/((s+2)^2)	inverselaplace\:\frac{s}{(s+2)^{2}}
(\partial)/(\partial x)(ye^x-xe^y)	\frac{\partial\:}{\partial\:x}(ye^{x}-xe^{y})
limit as x approaches 0+of 1/(e^x+1)	\lim\:_{x\to\:0+}(\frac{1}{e^{x}+1})
[3ln(x)-12sin(x)]	[3\ln(x)-12\sin(x)]
(\partial)/(\partial x)(ze^{x^2-y^2})	\frac{\partial\:}{\partial\:x}(ze^{x^{2}-y^{2}})
y^{''}-4y^'-4y=e^{2x}	y^{\prime\:\prime\:}-4y^{\prime\:}-4y=e^{2x}

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