MTH-2100 calculus 1 homework 3 questions.

MTH-2100 calculus 1 homework 3 questions.

page 136-137 # 7, 16, 21, 34
7) Find the derivative of the function
9=(4x-1)^3

16) Find the derivative of the function
f(x)=∛(12x-5)

21) Find the derivative of the function
9=1/√(3x+5)

34) Find the derivative of the function
9(x)=(2+(x^2+1)^4 )^3

page 153 # 5, 9, 16

5) A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given values of x.
9=2^(x^2 )+1; ⅆx/ⅆt=2 centimeters per second
(a)x=-1(b)x=O(c)x=1

9) consider a liner function y=ax+b if x changes at a rate, does y change at a consistent rate? Is so, does it change at the same rate as x? explain?

16) all edges of a cube are expanding at a rate of 6cm per second. How fast is the surface area changing when each edge is (a) 2cm (b) 10cm

page 325 # 42, 48, 53, 62

42) Find the derivative of the function
f(x)=ln⁡(x-1)

48) Find the derivative of the function.
y=M√(x^2-4)

53) Find the derivative of the function.
g(t)=In⁡t/t^2

62) Find the derivative of the function
9=ln⁡|csc⁡x |

page 343-344 # 23, 27, 33, 72

23) use the derivative to determine whether the function is strictly monotonic on its entire domain and therefore has an inverse function.
f(x)=2-x-x^3

27) use the derivative to determine whether the function is strictly monotonic on its entire domain and therefore has an inverse function.
f(x)=ln⁡(x-3)

33) show that f is strictly monotonic on the given interval and therefore has an inverse function on that interval.
f(x)=cos⁡x[0,π]

72) (a) find the domains of f and f^(-1) (b) find the range of f and f^(-1) (c) graph f and f^(-1) (d) show that slops of the graphs of f and f^(-1) are reciprocals at
the given points.
f(x)=3-4x

page 352 # 34, 38, 39, 46

34) find the derivative
y=ⅇ^(-8x)

38) find the derivative
y=5ⅇ^(x^2+5)

39) find the derivative
y=ⅇ^x ln⁡ x

46) find the derivative
y=ln⁡((1+ⅇ^x)/(1-ⅇx))

page 362 # 41, 44, 51

41) Find the derivative of the function
f(x)=x9^x

44) Find the derivative of the function.
f(t)=3^2t/t

51) Find the derivative of the function
9=log_5⁡√(x^2-1)

page 372 # 40, 43, 49

40) Find the derivative of the function
f(t)=〖arcsin t〗^2

43) Find the derivative of the function.
f(x)=arctan⁡ e^x

49) Find the derivative of the function.
y=2x arccos⁡X-2√(1-x^2 )

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