Base Derivatives
Find the first derivative of
y=x^3-4x+5
y'=3x^2-4
Find the first derivative of
y=cos(ln(x))
y'=(-sin(lnx))/x
Find dy/dx given
5x^2+2y^2=4x
dy/dx=(2-5x)/(2y)
Write the equation of a line tangent to
y=5x^3-x^2-10x
at x=2
y-16=46(x-2)
Find the first derivative of
f(x)=root(3)(x)-2e
f'(x)=1/(3root(3)(x^2)
Find the first derivative of
y=x^2e^(x^2)
y'=2xe^(x^2)+2x^3e^(x^2)
Find dy/dx given
x+x^2-3y^3=y^2
dy/dx=(2x+1)/(9y^2+2y)
Write the equation of a line tangent to
y=e^(2x+1)
at x=-1
y-0.37=0.74(x+1)
Find dy/dx given
y=lnx-cosx+2^x
dy/dx=1/x+sinx+2^xln2
Find dy/dx given
y=ln(2xe^x)
SIMPLIFY
dy/dx=(1+x)/x
Find dy/dx given
5x^3y+siny=2sinx
dy/dx=(2cosx-15x^2y)/(5x^3+cosy)
Find the absolute max and absolute min for
y=x^4-8x^2
on [-1,3]
Absolute Max: (3,9)
Absolute Min: (2,-16)
Find the first derivative of
g(x)=x^4tanx
g'(x)=4x^3tanx+x^4sec^2x
Find the first derivative of
f(x)=sin((3x^5)/(2x+1))
SIMPLIFY!
f'(x)=cos((3x^5)/(2x+1))\cdot((24x^5+15x^4)/(2x+1)^2)
Find dy/dx given
sin(xy^2)+3x^2=2y^3
dy/dx=(y^2cos(xy^2)+6x)/(6y^2-2xycos(xy^2)
Find all increasing/decreasing intervals for
f(x)=x^4/4-2x^3-18x^2+216x+300
Inc: (-6,6),(6,\infty)
Dec: (-\infty,-6)
Find dy/dx given
y=sqrt(x^4-2x^3)
(SIMPLIFY)
dy/dx=(2x^3-3x^2)/sqrt(x^4-2x^3)
Find f'(x) given
f(x)=e^[(2x^3)/cos(2x)]
f'(x)=e^[(2x^3)/cos(2x)]\cdot((6x^2cos(2x)+4x^3sin(2x))/cos^2(2x))
Find (d^2y)/(dx^2) given
3x^2-4y^3+y=2x+1
(d^2y)/(dx^2)=(-6(1-12y^2)^2+24y(2-6x)^2)/(1-12y^2)^3
Identify intervals of concave up/concave down for
y=x^6+3x^5-20x^4
Concave up: (\infty,-4),(2,\infty)
Concave down: (-4,0),(0,2)