Expert Answer to "Find the following higher-order derivatives. dndxn(2x)"

Reeves

Answered question

2021-04-14

Find the following higher-order derivatives.

\frac{d^{n}}{{d x}^{n}} (2^{x})

gotovub

Skilled2021-04-16Added 98 answers

Step 1:- Introduction:-
Given

\frac{d^{n}}{{d x}^{n}} (2^{x})

Step 2:- Calculation:-
Here

y = 2^{x}

2^{x} a s e^{x \ln (2)}

Thus

y = x^{x \ln (2)}

Differentiating with respect to x we get

\frac{d}{d x} (2^{x}) = \ln (2) 2^{x}

Again differentiating the above we get

\frac{d^{2}}{{d x}^{2}} = {(\ln (2))}^{2} 2^{x}

Thus we differentiate it upto n we get

\frac{d^{n}}{{d x}^{n}} = {(\ln (2))}^{n} 2^{x}

Step 3:- Conclusion:-
The answer is

{(\ln (2))}^{n} 2^{x}

Jeffrey Jordon

Expert2021-12-12Added 2605 answers

Answer is given below (on video)

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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