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Computing Derivatives
Computing Derivatives

Computing Derivatives: The Rules of the Game True or False

1. Let h(x) = e{3x + 7}. Which is the best choice for the inside function?

-> g(x) = ex.


2. The function h(x) is composed of two functions. The outside function is cos (□) and the inside function is ln x. Which formula best describes h? -> h(x) = cos x × ln x


3. The chain rule says that if h(x) = f(g(x)), then -> h'(x) = f(g'(x))f'(x)
4. Find the derivative of the function f(x) = (cos x)-3.

-> f'(x) = 3(cos x){-4}sin x


5. Suppose f and g are inverses so that f(g(x)) = x. Then

->


6. If s = 4t2 + 3 and r = cos s, then to find the derivative of s, then to find the derivative of r with respect to t we would use the version of the chain rule that says ->


7. The derivative of ln (5x6 + 7x2) is

->


8. Which function's derivative is -7sin(x)cos6 x?

-> cos7 x


9. Find y' given that y is a function of x and xy + x + y = 0

->


10. To use implicit differentiation on the equation we need to use -> the chain rule but not the product rule
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