### Blogging on Related Rates

Instead of reflecting, I'm going to list some information that might help you understand differentiating functions.

Constant Function f (x) = c f'(x) = 0

Constant Multiple Rule d/dx [c*f(x)] = c*f'(x)

Sum and Difference Rule d/dx[f(x) + g(x)] = f'(x) + g'(x) you can replace the + signs with a - sign

Power Rule d/dx(x^n) = nx^(n-1)

Derivative of e^x d/dx(e^x) = e^x

Exponential Function d/dx(a^x) = (ln a)*a^x

Product Rule d/dx[f (x)*g (x)] = f (x)*g'(x) + f'(x)*g (x)

Quotient Rule d/dx [f(x)/g(x)] = [g(x)*f'(x) - f(x)*g'(x)]/[g(x)]^2

Derivatives of Trigonometric Functions

d/dx (sin x) = cos x

d/dx (cos x) = -sin x

d/dx (tan x) = sec^2 x

d/dx (csc x) = -csc x cot x

d/dx (sec x) = sec x tan x

d/dx (cot x) = -csc^2 x

The Chain Rule [fog]' (x) = f'(g(x))*g'(x)

d/dx (ln x) = 1/x

Local linearization of f at x = a f (x) ~ f(a) + f'(a)(x-a)

All of these derivative rules are probably going to be on the test, so it is a good idea to learn how to use them. I excluded related rates because that depends on the question, and there is no definite formula for all related rates problems. These formulas and derivatives cover most of the unit and they are good to know.

Constant Function f (x) = c f'(x) = 0

Constant Multiple Rule d/dx [c*f(x)] = c*f'(x)

Sum and Difference Rule d/dx[f(x) + g(x)] = f'(x) + g'(x) you can replace the + signs with a - sign

Power Rule d/dx(x^n) = nx^(n-1)

Derivative of e^x d/dx(e^x) = e^x

Exponential Function d/dx(a^x) = (ln a)*a^x

Product Rule d/dx[f (x)*g (x)] = f (x)*g'(x) + f'(x)*g (x)

Quotient Rule d/dx [f(x)/g(x)] = [g(x)*f'(x) - f(x)*g'(x)]/[g(x)]^2

Derivatives of Trigonometric Functions

d/dx (sin x) = cos x

d/dx (cos x) = -sin x

d/dx (tan x) = sec^2 x

d/dx (csc x) = -csc x cot x

d/dx (sec x) = sec x tan x

d/dx (cot x) = -csc^2 x

The Chain Rule [fog]' (x) = f'(g(x))*g'(x)

d/dx (ln x) = 1/x

Local linearization of f at x = a f (x) ~ f(a) + f'(a)(x-a)

All of these derivative rules are probably going to be on the test, so it is a good idea to learn how to use them. I excluded related rates because that depends on the question, and there is no definite formula for all related rates problems. These formulas and derivatives cover most of the unit and they are good to know.

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