Learn to Find Derivatives: f(x) = 3cosx - (sinx/4) | Quotient Rule Explained

[physics=world]

1. f(x) = 3cosx - ((sinx)/(4))

Homework Equations

use the rules of differentiation3. i tried adding them together which i got

((12cosx - sinx) / (4))

then, i used quotient rule

((4)(-12sinx - cosx) - (12cosx - sinx)(0))/ (4^2)

which i got this for an answer

(-12sinx - cosx) /( 4)but the answer is
(-3sinx - cosx) /( 4)

 

[Mark44]

1. f(x) = 3cosx - ((sinx)/(4))

Homework Equations

use the rules of differentiation


3. i tried adding them together which i got

((12cosx - sinx) / (4))

then, i used quotient rule

((4)(-12sinx - cosx) - (12cosx - sinx)(0))/ (4^2)

which i got this for an answer

(-12sinx - cosx) /( 4)


but the answer is
(-3sinx - cosx) /( 4)

Neither of these is correct, assuming that the problem is as you posted.

If you are learning the quotient rule, you should also have learned some simpler rules, such as the sum rule and the constant multiple rule.

As a matter of course, you should never use the quotient rule if the denominator is a constant. It's not wrong to do so, but since the quotient rule is a bit on the complicated side, there is a greater chance of getting the derivative wrong due to an error of some sort.

 

[physics=world]

Neither of these is correct, assuming that the problem is as you posted.

If you are learning the quotient rule, you should also have learned some simpler rules, such as the sum rule and the constant multiple rule.

As a matter of course, you should never use the quotient rule if the denominator is a constant. It's not wrong to do so, but since the quotient rule is a bit on the complicated side, there is a greater chance of getting the derivative wrong due to an error of some sort.

ohh. thanks i see what i did wrong.