derivative rules

a lot of these are written for me to understand them better!

constant rule

the derivative of any constant is 0

power rule

[x^n']’=nx^n-1

derivative of e^x

e^x stays the same, only if the x is alone!

derivative of e^kx, where k is a constant

ke^-kx bring constant to the front, but the exponent stays the same!

derivative of a^x, for any positive constant a

(lna)a^x (ln the constant times the original function)

derivative of lnx

1/x

derivative of sin x

cos x

derivative of cos x

-sin x

derivative of sin(kx) for any constant k

kcos(kx)

derivative of cos(kx) for any constant k

-sin(kx)

chain rule!!

derivative of outside function times the derivative of the inside function

product rule

[fg]’=f’g+fg’ sandwich plus side!

quotient rule

[f/g]’=f’g-fg’/g² sandwich minus side all over g sqared

when given a fraction with an exponent in the denominator…

put numerator in front and change the sign of the exponent, then use power rule to find the derivative example: 3/t²=3t^-2

limit definition of the derivative

f’(x)= lim h approaching 0 f(x+h)-f(x) / h