Finding Derivative of a function?

Question

Ok. The problem I am not understanding is finding the derivate of a function like - x^4 / 2

With a function like y = 1 / x^2 the derivative comes out to - 2 / x^3

y = 1 / x^2

y = x ^ -2

dy/dx = (-2)x^-3

dy/dx = - 2 / x^3

but I cant seem to find the derivate where the x is on the top.

How do I get - x^4 / 2 ?

Answer 1

It's even simpler. Just remember that, for every real a, the derivative of f(x) = x^a is f'(x) = a* x^(a-1).

In your case, f(x) = -x^4/2 = (-1/2)(x^4). Therefore, f'(x) = (-1/2) *4x^3 = -2x^3.

Answer 2

The derivative of -1/2 x^4 is -4/2 x^3 or -2x^3

Answer 3

Hehe. Its much easier, though!

(x^n)' = n x^(n-1)

And, if you have a constant,

(k x^n)' = n k x^(n-1)

So: if you have a -x^4 /2, its (-1/2)x^4, and -1/2 is a constant

You only have to take the derivative of x^4 and its equals to 4 x^3

The derivative of x^3 is 3 x^2

The derivative of x^18 is 18 x^17

etc

The derivative or 15 x^3 is 15 * 3 x^2 = 45 x^2

Ana

Answer 4

Seperate the (1/2) so the equation looks like
(-x^4)*(1/2)
The derivative becomes
(-4)(x^3)*(1/2)
(x^3)(-2)

Answer 5

y = 1/x^2 <-- try transferring the denominator to the numerator

y= 1(x^(-2)) <-- once you transferred x raised to 2 to the numerator... it will become x raise to negative 2.

y= x^(-2) <-- u could now derive it by..multiplying the whole equation to the exponent

(-2) (x^(-2))<-- then subtract one from the exponent

dy/dx = -2 (x^(-3)) <--- to remove the negative exponent .. bring x to the denominator

dy/dx = -2/ (x^3) <-- making the exponent positive..



NOw try doing it to -x^4 /2

-x^4 /2 <-- multiply it all to 4 and subtract one from the exponent

-4 x^3 / 2 <- simplify

-2x^3

the formula for this is

x^n ==> multiply n to the equation .. then subtract one from the exponent

nx^ (n-1)



if you're asked to differentiate (12 x^2 ) / 2

(try solving it)

youll get

12x

Answer 6

the derivatave of -x^4/2:

can be re written as -1/2*x^4

differentiating we get (4)(-1/2)x^3 = -2x^3