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(d)/(dx)[log(e)e^(sin(x^(2)))] is equal ...

`(d)/(dx)[log_(e)e^(sin(x^(2)))]` is equal to

A

` 2 cos (x^(2))`

B

`2 cos x `

C

`2x . Cos x `

D

`2x cos (x^(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)/(dx) [ log_(e) e^(sin(x^(2)))]= (d)/(dx) [ sin (x^(2))] = cos (x^(2)) 2x `
` [ because log_(e) e^(f(x)) = f(x)]`
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  12. If x=(1-sqrt(y))/(1+sqrt(y)) then (dy)/(dx) is equal to

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  13. If y = log (sin (x^(2))), 0 lt x lt (pi)/(2), "then " (dy)/(dx) "at ...

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  14. (d)/(dx)[log(e)e^(sin(x^(2)))] is equal to

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  15. If y=sqrt((1-x)/(1+x)), then (1-x^(2))(dy)/(dx)+y is equal to

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