Spring ’05/MAT 250/Exam 2 Name: Show all your work.
Differentiate and simplify where appropriate:
1. (4pts) d
dx (7x3−4x+3
√x2+c4) =
2. (4pts) d
dx (xln x−x) =
3. (5pts) d
dx cos √x2−5x+ 10 =
4. (5pts) d
dx
x
√x2+ 5 =
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Practice Exam 2 - Spring 2005 - Calculus and Analytic Geometry I | MAT 250, Exams of Analytical Geometry and Calculus
Material Type: Exam; Class: Calculus and Analytical Geometry I; Subject: MAT Mathematics; University: Murray State University; Term: Unknown 1989;
Typology: Exams
Pre 2010
1 / 4
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Spring ’05/MAT 250/Exam 2 Name: Show all your work.
Differentiate and simplify where appropriate:
- (4pts)
d dx
(7x^3 − 4 x^ + 3
x^2 + c^4 ) =
- (4pts)
d dx
(x ln x − x) =
- (5pts)
d dx
cos
x^2 − 5 x + 10 =
- (5pts)
d dx
x √ x^2 + 5
- (5pts) Use logarithmic differentiation to find
d dx
xtan^ x.
- (4pts) Find the first three derivatives of f (x) and use them to find the formula for f (n)(x) if f (x) = ex(x + 5).
- (6pts) Use implicit differentiation to find y′.
exy^ = x^2 + y^4
- (7pts) A plane flying horizontally at an altitude of 1mi and a speed of 500mi/hr passes directly over a radar station. Find the rate at which the straight-line distance from the plane to the radar station is increasing when this distance is 2mi.
Bonus. (5pts) Verify that
d dx
2 x^2 − 1 4
arcsin x +
x
1 − x^2 4
= x arcsin x.