Derivative

[psi20]

If you have f(x) = e^(-.25x + 2)

 

is the derivative e^(-.25x + 2) ? If not, what is it?

[timo]

No it isn´t. Do you know the chain-rule?

[psi20]

No, I don't know anything except f'(x) = (f(x+h) - f(x))/h lim h--> 0 or something.

[rakuenso]

edit

 

f(x) = e^(-.25x + 2)

f'(x) = e^(-.25x+2)*d/dx[-.025x+2]

f'(x) = -.025x(e^(-.025x+2))

[P_Rog]

d/dx[-.25x+2] = -.25

[MandrakeRoot]

Simple rules for real valued differentiable functions :

 

(f(x) g(x))' = f'(x) g(x) + f(x) g'(x)

(f(x) + g(x))' = f'(x) + g'(x)

[f(g(x))]' = f'(g(x))g'(x)

 

Try showing their correctness with the definition of the derivative :

Remember that a function f is differentiable at x if the following limit exists

[math]\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}[/math]

If so then the value is denoted f'(x)

 

Mandrake

[rakuenso]

d/dx[-.25x+2'] = -.25

 

oops =P