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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)), thenh'(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 usethe chain rule but not the product rule