10. Let f(x) = sin(2x + 1) and g(x) = x3 + 3 for all real x. Which of the following is equal to the derivative of the composite function f[g(x)]?
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A. sin(2x3 + 7) |
B. cos(2x3 + 7) |
C. 6 sin(2x3 + 7) |
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D. 6 cos(2x3 + 7) |
E. 6x2 cos(2x3 + 7) |
Solution: The answer is E
First find the composite function f[g(x)] and then differentiate with respect to x.
The composite function f[g(x)] is defined as,
Use the Chain Rule to differentiate with respect to x as follows,
