Uploaded by TheIntegralCALC on 12.02.2010

Transcript:

Hey everyone!

What's up?

Another derivative problem,

this one is slightly more complicated,

but only slightly,

f(x) = 100 - 16x^2.

The last derivative problem we did didn't have an exponent, now we've got an exponent.

So, derivative notation, f'(x)

equals...

As we've learned last time the derivative of a constant is 0,

so that goes away,

and then, all we have to deal with is this 16x^2 here.

We'll also have to keep in mind that there's a... there's a negative in front of it.

So the way that we're going to take the derivative of this,

as before, is the exponent times the coefficient.

So it's going to be 2 times 16.

Oh, I can see I already made a mistake, I... I forgot the negative sign,

so, we have to put the negative sign in front of it here,

and then the exponent times the coefficient, 2 times 16,

the x we keep, and we subtract 1 from the exponent,

so 2 - 1 is 1.

And then, we just simplify this,

the derivative is negative,

2 times 16, 32,

x, and then we can just drop the 1 obviously as the exponent,

so -32x here is our answer.

See you later!

What's up?

Another derivative problem,

this one is slightly more complicated,

but only slightly,

f(x) = 100 - 16x^2.

The last derivative problem we did didn't have an exponent, now we've got an exponent.

So, derivative notation, f'(x)

equals...

As we've learned last time the derivative of a constant is 0,

so that goes away,

and then, all we have to deal with is this 16x^2 here.

We'll also have to keep in mind that there's a... there's a negative in front of it.

So the way that we're going to take the derivative of this,

as before, is the exponent times the coefficient.

So it's going to be 2 times 16.

Oh, I can see I already made a mistake, I... I forgot the negative sign,

so, we have to put the negative sign in front of it here,

and then the exponent times the coefficient, 2 times 16,

the x we keep, and we subtract 1 from the exponent,

so 2 - 1 is 1.

And then, we just simplify this,

the derivative is negative,

2 times 16, 32,

x, and then we can just drop the 1 obviously as the exponent,

so -32x here is our answer.

See you later!