Question

a) sinx b) cosx c)sinhx d) log_e(x) which of the following does not change its form after that three successive differentiation
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Answer 1

Answer:

a.sinx

Step-by-step explanation:

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Answer 2

None of these.

Concept:

Differentiation is a technique for determining a function's derivative. Differentiation is a mathematical procedure for determining the instantaneous rate of change of a function depending on one of its variables.

Given:

The terms sinx, cosx, sinhx and $log_{e} x$.

Find:

The term that does not change after three successive differentiation.

Solution:

1st differentiation of sinx is = cosx.

2nd differentiation of sinx is = -sinx.

3rd differentiation of sinx is = -cosx.

Hence, Option (A) is incorrect.

1st differentiation of cosx is = -sinx.

2nd differentiation of cosx is = -cosx.

3rd differentiation of cosx is = sinx.

Hence, Option (B) is incorrect.

1st differentiation of sinhx is = coshx.

2nd differentiation of sinhx is = sinhx.

3rd differentiation of sinhx is = coshx.

Hence, Option (C) is incorrect.

1st differentiation of $log_{e} x$ = $\frac{1}{x}$.

2nd differentiation of $log_{e} x$ = $\frac{-1}{x^2}$.

3rd differentiation of $log_{e} x$ =$\frac{2}{x^3}$.

Hence, Option (D) is incorrect.