Derivatives
f(x) = x2⋅sin(x)
Find f'(x).
2xsin(x) + x2cos(x)
Find dy/dx.
y2 = x3+y
3x2/(2y-1)
A spherical balloon is being inflated such that the volume is increasing at a rate of 50 cm³/s. How fast is the radius increasing when the radius is 10 cm?
1/8π cm3/s
f(x) = ex
Find f'(x).
ex
f(x) = ln(x)
Find f'(x).
1/x
f(x) = (3x2+1)/x
Find f'(x).
(3x2-1)/x2
Find dy/dx.
sin(y)=x2+2y
2x/cos(y)-2
A ladder 10 meters long is leaning against a wall. The bottom of the ladder is being pulled away from the wall at 1 m/s. How fast is the top of the ladder sliding down the wall when the bottom is 6 meters away?
-3/4 m/s
f(x) = e3x
Find f'(x).
3e3x
f(x) = ln(3x)
Find f'(x).
1/x
f(x) = (2x3+5)4
Find f'(x).
24x2(2x3+5)3
Find dy/dx.
x2+y2=25
-x/y
Air is being pumped into a spherical balloon, causing its radius to increase at a rate of 2 cm/s. How fast is the volume of the balloon increasing when the radius is 5 cm?
200π cm3/s
f(x) = x2ex
Find f'(x).
2xex+x2ex
f(x) = xln(x)
Find f'(x).
f(x) = sin(x)/x2
Find f'(x).
cos(x)/x2 - 2sin(x)/x3
Find dy/dx.
ey=x2+y3
2x/(ey-3y2)
A spotlight is shining on a wall. If a man 2 meters tall walks away from the wall at 1.5 m/s, how fast is the length of his shadow on the wall increasing when he is 4 meters from the wall?
3/4 m/s
f(x) = e2x
Find f''(x).
4e2x
f(x) = ln((x-3)/(x+7)^1/3)
Find f'(x).
1/(x-3) - 1/[3(x+7)]
f(x) = ln(x2+1)⋅e3x
Find f'(x).
2x/(x2+1)⋅e3x + ln(x2+1)⋅3e3x
Find dy/dx.
cos(xy)=x+y
[1+ysin(xy)]/-(xsin(xy)+1)
A conical tank is being filled with water at a rate of 5 m³/min. The tank has a height of 10 meters and a radius of 4 meters. How fast is the water level rising when the water is 6 meters deep?
125/144π
f(x) = ex/x
Find f'(x).
[ex(x-1)]/x2
f(x) = ln [((2x+2)2(x4-3)5)/(x-2)2]
Find f'(x).
4/(2x+2) + 20x3/(x4-3) - 2/(x-2)