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Computing Derivatives

Computing Derivatives

Computing Derivatives: The Rules of the Game True or False

1. Let h(x) = e3x + 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 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