Calculus 1 Review

Derivative Rules

100

What is the product rule?

f'g+g'f

200

What is the quotient rule?

f'g-g'f/ g²

300

What is the derivative of log_ax?

1/x times 1/x

400

Write the chain rule

(f’ º g) × g’

Trig Derivatives

100

Derivative of sinx

cosx

200

Derivative of tanx

sec²x

300

Derivative of tan^-1x

1/(1+ x²)

400

Derivative of sin^-1(x³)

3x²/  (1-x⁶)^1/2

General Derivative

100

What is the derivative of the function f(x) = ln(x²+ 1)?

a) 2x / (x² + 1)

200

What is the derivative of the functionf(x)=sqr(x)/ x^2?

d) (1 + 2x) / (2x^3)

Hard Problems on Quizzes I Failed

100

. What is the derivative of the function

 f(x) = e^x  / x² ?

c) (e^x - 1) / (x³)

200

If f(x)= x²-4, and g is a differentiable function of x, what is the derivative of f(g(x))

2g'(x)

300

The limit does not exist