Differentiation

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Across
  1. 2. average rate of change of a function over some two intervals; (f (a+h) -f(a)) /h
  2. 7. (d/dx)(c)=0
  3. 8. involve multiple quantities that are changing in relation to each other; uses derivatives, and especially the chain rule to solve problem
  4. 12. derivative of sinx
  5. 13. y'=f'(g(x))*g'(x)
  6. 14. d/dx[f(x)-g(x)]=f'(x)+g'(x)
  7. 15. 1/xsqrt(x^2-1)
  8. 16. d/dx[cf(x)]=cf'(x)
Down
  1. 1. d/dx[f(x)-g(x)]=f'(x)-g'(x)
  2. 3. is the process of finding the derivative dy/dx for such functions, and it is accomplished by applying the chain rule
  3. 4. d/dx[f(x)g(x)]=f'(x)g(x)+f(x)g'(x)
  4. 5. 1/sqrt(1-x^2)
  5. 6. the derivative of the function is 1/x
  6. 9. d/dx[f(x)/g(x)]=(f'(x)g(x)-f(x)g'(x))/[g(x)]^2
  7. 10. derivative of secx
  8. 11. (d/dx)(x^n)=nx^n-1, for any real number n