Calculus

Derivatives

100

Find the derivative of 7x⁴+9x³-27x²-13x+e^x+1

28x³+27x²-54x-13+e^x

200

Find the derivative of cos(x² + 3x) + 15x

-(2x +3)(sin(x² + 3x)) +15

300

Find the derivative of 

(15x^2-e^x+5)/(3x+2)

((3x+2)(15x-e^x)-(15x^2-e^x+5)(3))/((3x+2)^2)

400

Find the derivative of 

Arctan(cos(34x^2-13x+5)))

(-(68x-13)(sin(34x^2-13x+5)))/(1+cos^2(34x^2-13x+5))

500

Find the derivative of 

(cos(x^2+5x)-17x^2-13x)/(sin(x^2+2))

((sin(x^2+2)*-(2x+5)(sin(x^2+5x)-34x-13)-((cos(x^2+5x)-12x^2-13x)*2xcos(x^2+2)))/sin^2(x^2+2)

Integrals

100

int \ x^3-3x^2+9x-5 \ dx

x^4/4-x^3+(9x^2)/2+5x+C

200

int_0^5 15x^2-17x+2 \ dx

845/2

300

int_(pi/6)^(pi/2) \ (xcosx-4)/x

1/2-4ln(pi/2)+4ln(pi/6)

400

int \ x^2/ sqrt(1-x^6) \ dx

1/3sin^-1x^3+C

500

int_1^3 1/x^2 sqrt (1- 1/x) \ dx

(2/3)^(5/2)

limits

100

lim_(x->1) x^2

1

200

lim_(x->1)(x^2-2x+3)/(4x)

1/2

300

lim_(x->0) (x^2+5x)/x

5

400

lim_(x->oo) arctanx

pi/2

500

lim_(x->1^+) (x^2-3x)/(x-1)

-oo

Velocity

100

Find the velocity of s(t)=15x-5 where s is in ft and t is in sec

15 ft/sec

200

Velocity of s(t)=

15x^3+18x^2-9

 where s is in and t is in min

45x^2+36x

300

find v(t) if a(t)=

 14x^3+5x^2+3 in/min²

and v(0)=7

v(t)=

 (7t^4)/2+(5t^3)/3+3t+7 in/min

400

Find net displacement of  t^3+2t^2-8t m/s, from -2 to 3

 235/12 m

500

Find total distance of  t^3+2t^2-8t m/s from -2 to 3

 395/12 m

Random

100

Continuity: y=

(x-3)/(x^2-9x+18)

, find any holes

X=3

200

g(x) = 

 int_0^x 3t^2-1 find g'(x)

3x^2-1

300

find the slop tangent to the curve  y^3x+y^2x^2=6  at (2,1)

-15/4

400

Related rates: A 5m ladder is leaning against a wall. If the lower end of the ladder slides away from the wall at a rate of 0.5m/s, what rate is the inclination of the ladder with respect to the ground changing when the lower end of the ladder is 4m away from the wall? 

Decreasing at a rate of 1/6 rad/sec

500

The base of a solid is the region bounded by the graphs of y=

3sqrt(3x)

and y=

x^2

. Find the volume of the solid if slices perpendicular to the x-axis are equilateral triangles. 

4.50952