Can someone please help me with this?
f(x)=(x-2)^1/2 * (x^2-3)^3 find f'(x) using the product rul.
This is what I came up with I just need to know if I did it right.
f'(x)=(x-2)^1/2*3(x^2-3)+(x^2-3)^3*(1)^-1/2
Hopefully I did. Thanks.
no. You are not using the chain rule..
If f(x)=g(x) * h(x) then
f'(x)=g(x) * h'(x) + g'(x) * h(x)
now if h(x)= (x-2)^.5 then
h'(x) =.5 * (x-2)^-.5 *1
and if g(x)=(x^2-3)^3 then
g'(x)=3(x^2-3)^2 *(2x)
what is the product rule? Explain and provide an example
what is the product rule? Explain and provide an example
Please help me with dis problem....
Y=(2-5x)^2
The product rule is a differentiation rule used to find the derivative of a function that is the product of two other functions. It is often used when we have a function that cannot be easily differentiated directly.
The product rule states that if we have two functions, u(x) and v(x), their product f(x) = u(x) * v(x) can be differentiated using the following formula:
f'(x) = u(x) * v'(x) + v(x) * u'(x)
In simple terms, this means that to find the derivative of a function that is the product of two other functions, we differentiate one function and multiply it by the other, then differentiate the second function and multiply it by the first, finally adding the two together.
Here's an example to help illustrate the product rule:
Let's say we have the function f(x) = x^2 * sin(x). To find the derivative f'(x) using the product rule, we differentiate each part separately.
Let u(x) = x^2 and v(x) = sin(x).
Now let's find the derivatives:
u'(x) = 2x (by power rule) and v'(x) = cos(x) (by derivative of sine).
Applying the product rule:
f'(x) = u(x) * v'(x) + v(x) * u'(x)
= (x^2) * (cos(x)) + (sin(x)) * (2x)
So, the derivative of f(x) = x^2 * sin(x) is f'(x) = x^2 * cos(x) + 2x * sin(x).
Make sure to check your calculation once again using the corrected product rule approach.