Calculus derivative memorization

k times f’(x)

What is the derivative for k times f(x)?

e^x

What is the derivative for e^x?

-1/(x²)

What is the derivative for 1/x?

-k/x²

What is the derivative for k(constant)/x?

1 over 2 times√x 

What is the derivative for the square root x?

1/ 2(√x+k) or 1/ 2 times the square root of x plus k

what is the derivative for the square root of x+k?

n/ 2 times the square root of x plus k

what is the derivative for n times the square root of x + k? 

f’(x) times g(x) - g’(x) times f(x) all over [g(x)]²

What is the quotient rule?

cos(x)

what is the derivative for sin (x)?

-sin(x)

what is the derivative for cos(x)?

sec²x

what is the derivative for tan(x)?

-csc²x

what is the derivative for cot(x)?

sec(x) times tan(x)

what is the derivative for sec(x)?

-csc(x) times cot(x)

what is the derivative for csc(x)?

(f’(x) times g(x)) times g’(x)

what is the chain rule?

f(x) times g’(x) + g(x) times f’(x)

what is the product rule?

1 over (square root of 1-x²)

what is the derivative for sin^-1(x)?

-1 over (square root 1-x²)

what is the derivative for cos^-1(x)? 

1 over (1 +x²)

what is the derivative for tan^-1(x)?

-1 over (1 +x²)

what is the derivative for cot^-1(x)?

k times 1/(x)

what is the derivative for ln(x), but with k(constant) times ln(x)?

1/g(x) times g’(x)

what is the derivative for ln(g(x))?