# How do you differentiate #f(x)=(x)*(x)-2x^2# using the product rule?

Write it as

By signing up, you agree to our Terms of Service and Privacy Policy

To differentiate ( f(x) = x \cdot x - 2x^2 ) using the product rule, follow these steps:

- Identify the two functions being multiplied: ( x ) and ( x - 2x^2 ).
- Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function, plus the first function times the derivative of the second function.
- Differentiate the first function, ( x ), which results in 1.
- Differentiate the second function, ( x - 2x^2 ), which results in ( 1 - 4x ).
- Apply the product rule formula: ( (1)(x - 2x^2) + (x)(1 - 4x) ).
- Simplify the expression obtained in step 5 to get the derivative of ( f(x) ).

The derivative of ( f(x) = x \cdot x - 2x^2 ) using the product rule is ( f'(x) = x - 4x^2 + 1 ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the derivative of #y = (2x+3)^4 / x#?
- How do you differentiate #g(x) = (1/x^3)*sqrt(1-e^(2x))# using the product rule?
- How do you differentiate #f(x) = x*e^(x^2)*sin(x^2)# using the product rule?
- How do you differentiate #f(x)= x^3 (1-3x^2)^4 # using the product rule?
- How do you differentiate #f(x) =(x^2+1)(x-3)^3# using the product rule?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7