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How do you differentiate #f(x) = 2x cos(x²)#?

Answer 1

Scarlett Allison

Refer to explanation

It is

#(df)/(dx)=2*cos(x^2)-2x*sin(x^2)*(2x)=2cos(x^2)-4x^2*sin(x^2)#

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Answer 2

Emma Aldridge

To differentiate the function f(x) = 2x cos(x²), you can use the product rule.

Let u(x) = 2x and v(x) = cos(x²). Then, differentiate both u(x) and v(x) separately.

u'(x) = 2 v'(x) = -2x sin(x²)

Now, apply the product rule:

f'(x) = u(x)v'(x) + v(x)u'(x)

f'(x) = (2x)(-2x sin(x²)) + cos(x²)(2)

Simplify:

f'(x) = -4x² sin(x²) + 2cos(x²)

So, the derivative of f(x) = 2x cos(x²) is f'(x) = -4x² sin(x²) + 2cos(x²).

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Answer from HIX Tutor

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.