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Find the second derivative of excosx
- a)-2exsinx
- b)-exsinx
- c)ex(sinx + cosx)
- d)-2excosx
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Find the second derivative of excosxa)-2exsinxb)-exsinxc)ex(sin...
**Solution:**
To find the second derivative of the given function, we need to differentiate it twice with respect to x.
First, let's find the first derivative of the function:
f(x) = ex * cosx
Using the product rule, the derivative of f(x) is:
f'(x) = (ex * (-sinx)) + (cosx * ex)
= -ex * sinx + ex * cosx
= ex * (cosx - sinx)
Now, let's find the second derivative of the function. Taking the derivative of f'(x):
f''(x) = (ex * (-sinx)) + (ex * (-cosx))
= -ex * sinx - ex * cosx
= -ex * (sinx + cosx)
Therefore, the second derivative of excosx is -2exsinx, which is option A.
To find the second derivative of the given function, we need to differentiate it twice with respect to x.
First, let's find the first derivative of the function:
f(x) = ex * cosx
Using the product rule, the derivative of f(x) is:
f'(x) = (ex * (-sinx)) + (cosx * ex)
= -ex * sinx + ex * cosx
= ex * (cosx - sinx)
Now, let's find the second derivative of the function. Taking the derivative of f'(x):
f''(x) = (ex * (-sinx)) + (ex * (-cosx))
= -ex * sinx - ex * cosx
= -ex * (sinx + cosx)
Therefore, the second derivative of excosx is -2exsinx, which is option A.
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Find the second derivative of excosxa)-2exsinxb)-exsinxc)ex(sin...
Please differentiate twice
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