Question

If f(x) = xcosx, then f'(0) is

Answer 1

Answer:

given: f(x) = x cos x

to evaluate f'(0)

let y = x cos x

f' = x * (-sinx) + cos x * 1 [ product rule ]

=> f' = - x sin x + cos x

=> f' = cos x - x sin x

=> f'(0) = cos 0 - 0*sin 0

=> f'(0) = 1 - 0*0

=> f'(0) = 1

Answer 2

If f(x) = xcosx, then f'(0) is 1

Given :

f(x) = xcosx

To find :

The value of f'(0)

Solution :

Step 1 of 3 :

Write down the given function

The given function is

f(x) = xcosx

Step 2 of 3 :

Find the derivative

f(x) = xcosx

Differentiating both sides with respect to x we get

f'(x) = - x sinx + cosx

Step 3 of 3 :

Find the value

f'(x) = - x sinx + cosx

Putting x = 0 we get

f'(0) = - 0 sin0 + cos0

⇒ f'(0) = 0 + 1

⇒ f'(0) = 1

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