Derivative Rules

Question 1

Product Rule

Answer 1

f’(x)g(x) + f(x)g’(x), The derivative of the first times the second plus the first times the derivative of the second

Question 2

Reciprocal Rule

Answer 2

[-g’(x)]/[g(x)]^2, The negative of the derivative of the denominator over the denominator squared

Question 3

Chain Rule

Answer 3

f’(g(x))g’(x), Derívate of the outside times the derivative of the inside

Question 4

Quotient Rule

Answer 4

[f’(x)g(x) - f(x)g’(x)]/[g(x)]^2, The derivative of the numerator times the denominator minus the numerator time the derivative of the denominator all over the denominator squared

Question 5

Derivative of lnx

Answer 5

1/x or, if the function is lnu, u’/u

Question 6

Derivative of e^x

Answer 6

e^x or, if the function is e^u, (e^u)u’

Question 7

Derivative of Inverse Functions

Answer 7

If g(x) is the inverse of f(x), then g’(x)=1/f’(g(x))

Question 8

Derivatives of Bases Other than e

Answer 8

d/dx(a^x)=a^x
d/dx(a^u)=u’(a^u)lna
d/dx(log[a]x)=1/xlna
d/dx(log[a]u)=u’/ulna