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Home / Calculus I / Derivatives / Differentiation Formulas
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Section 3.3 : Differentiation Formulas

For problems 1 – 20 find the derivative of the given function.

  1. g(x)=84x3+2x8
  2. f(z)=z107z5+2z3z2
  3. y=8x410x39x+4
  4. f(x)=3x4+x43x
  5. R(t)=9t10+8t10+12
  6. h(y)=3y68y3+9y1
  7. g(t)=t7+2t36t2+8t41
  8. z=6x74x+3x
  9. f(x)=79x422x7+3x4
  10. h(y)=6y+6y5+79y2
  11. g(z)=4z2+17z512z
  12. y=23t9+17t39t2t3
  13. W(x)=x31x6+15x2
  14. g(w)=(w5)(w2+1)
  15. h(x)=x(19x3)
  16. f(t)=(32t3)2
  17. g(x)=(1+2x)(2x+x2)
  18. y=48x+2x2x
  19. Y(t)=t42t2+7tt3
  20. S(w)=w2(2w)+w53w

For problems 21 – 26 determine where, if anywhere, the function is not changing.

  1. f(x)=2x39x2108x+14
  2. u(t)=45+300t2+20t33t4
  3. Q(t)=t39t2+t10
  4. h(w)=2w3+3w2+4w+5
  5. g(x)=9+8x2+3x3x4
  6. G(z)=z2(z1)2
  7. Find the tangent line to f(x)=3x54x2+9x12 at x=1.
  8. Find the tangent line to g(x)=x2+1x at x=2.
  9. Find the tangent line to h(x)=2x84x at x=16.
  10. The position of an object at any time t is given by s(t)=3t444t3+108t2+20.
    1. Determine the velocity of the object at any time t.
    2. Does the position of the object ever stop changing?
    3. When is the object moving to the right and when is the object moving to the left?
  11. The position of an object at any time t is given by s(t)=1150t3+45t42t5.
    1. Determine the velocity of the object at any time t.
    2. Does the position of the object ever stop changing?
    3. When is the object moving to the right and when is the object moving to the left?
  12. Determine where the function f(x)=4x318x2336x+27 is increasing and decreasing.
  13. Determine where the function g(w)=w4+2w315w29 is increasing and decreasing.
  14. Determine where the function V(t)=t324t2+192t50 is increasing and decreasing.
  15. Determine the percentage of the interval [6,4] on which f(x)=7+10x35x42x5 is increasing.
  16. Determine the percentage of the interval [5,2] on which f(x)=3x48x3144x2 is decreasing.
  17. Is h(x)=3x+x2+2x3 increasing or decreasing more on the interval [1,1]?
  18. Determine where, if anywhere, the tangent line to f(x)=12x29x+3 is parallel to the line y=17x.
  19. Determine where, if anywhere, the tangent line to f(x)=8+4x+x22x3 is perpendicular to the line y=14x+83.
  20. Determine where, if anywhere, the tangent line to f(x)=3x8x is perpendicular to the line y=2x11.
  21. Determine where, if anywhere, the tangent line to f(x)=13x9+1x is parallel to the line y=x.